I have been on eBay for years now, and know most of the in's and out's of how things work here.  I have recently gotten into coin collecting, and of course have found that eBay is a great place to find coins and to help build my collection.  Condition of coins is of course very important in coin collecting, and buying things 'sight unseen' can be worrisome.  I have been able to put my knowledge of eBay and possible pitfalls to avoid to prevent myself from being taken advantage of, and I would like to share these with you.

Tips for buying coins:

1. Pictures, pictures, pictures.  If an auction for coins/bills does not have any pictures of what you're buying, then either pass it by or assume the coins/bills are of very low quality.  Also, avoid "stock photo" pictures.  This might happen when someone is selling multiple lots that consist of the same kinds of coins, so they just took a picture of one of the lots and are using it for each of their auctions with the disclaimer "picture is not necessarily of the actual coins you will receive" or something similar.  You know they picked out the coins in the best condition for the picture, so chances are you'll be getting coins that are in worse shape than the ones shown.  Also, be wary of auctions that only have pictures of one side of the coin.  There might be a reason why the other side isn't pictured.
2. "Grab Bag" and other like lots.  You'll see many auctions that state "We found a bunch of coins at an estate sale and are dividing them into equal lots" or "We found cigar boxes full of coins in an abandoned attic", etc.  They state that they just grab a handful of coins and send them out without searching through them and that this is your big chance to get a bunch of great coins for a low price.  Usually, they'll throw in a little incentive such as "We have thrown in a gold coin in every 50th lot".  Unless you are a big time gambler, avoid these auctions.  As they say with most casino games, the odds are with the house.  Don't fall for the possible dreams of pulling that "$10,000" coin out of one of their lots, or whatever else they try to sell.  Chances are over 90% that you'll just barely get your bid back in coins, and once you add shipping charges onto that you'll lose out.  Also, if someone is selling "50 Buffalo Nickel" or a large quantity of another kind of coin but doesn't list the years/mint marks of the coins included then you have to assume that they're either all common coins for that set or contain many duplicates, or both!
3. "Graded" coins.  Be weary of auctions where the seller grades the coins themselves by saying something like "I'd grade this coin as VF" or "This is your chance to obtain this AU coin", but then usually in the small print they'll say "coin grades are just my opinion" to cover themselves.  Grading can be very objective and usually a seller will grade a coin at least slightly higher than is should be.  Unless the coins are slabbed and graded by a professional eBay approved grading service, disregard any gradings.  If the grading service is listed and you are not familiar with their work, do some internet and/or eBay guide searches on them to see about their legitimacy.
4. Seller Feedback.  As with any seller, reviewing their past feedback can tell a lot about their products.  This can be tricky though, because most sellers will not leave feedback for the buyer until the buyer has left it for them . . . which makes some buyers a little hesitant to leave negative feedback for fear of unfairly receiving negative feedback in return.  If they have negative feedbacks on auctions similar to the one you are considering then I'd definately avoid them.  If they have a bunch of positive feedbacks with comments like "ok coins" or "decent transaction" or other similar comments then that could be cause for concern as well.  I think you can get a good vibe about the seller by reading all of their comments, both positive and negative.  I generally start to worry if the seller for auctions I am looking has a feedback rating of less than 99%.  Another thing to keep in mind regarding feedback are "glowing" feedback comments left by "buyers" with very few eBay transactions.  It has been known that some sellers on eBay have "dummy" accounts that they use to "buy" some of their items (usually grab bags) and leave comments like "Wow, I found a 1909-S VDB Lincoln!!" or "Incredible finds!! Best Grab Bag ever!!".  If there are too many of those, something might be up.
5. Single coin auctions vs multiple coin auctions.  Generally, I avoid single coin auctions for coins that aren't that expensive, like most indian head/wheat pennies or buffalo/liberty nickels, etc.  This is where shipping charges can sneak up on you if you buy individually rather than in lots.  Say person A buys 20 indian head coins in 20 separate auctions for a total of $20 and person B buys 20 indian head coins from 2 auctions for a total of $25.  Who usually makes out better?  If person A somehow only got charged $1 shipping per auction (which would be on the cheap end) then their total would be $40.  If person B got charged $10 for shipping (which would be on the high end) their total would be $35.  Buying coins in lots definately saves you money in the long run.  The only time I purchase coins from single coin auctions is if the coin is somewhat valuable (usually $10 or more) and has cheap enough shipping where the total + shipping comes in around the coin value, or if the seller is selling more than a few coins I need AND combines shipping.
6. Replicas and copies.  If the price of a coin/bill seems too good to be true, it just might be.  Search the auction page for the word "Replica" or "Copy".  A lot of the more valuable coins have had replicas made at one time or another, and some people might try to get sneaky and only mention that a coin is a replica in one place in the description.  Most auctions clearly list that the coin is a replica or a copy, but it's something to keep in mind.
7. Shipping charges/information.  As with any auction, make sure the shipping charges are stated.  What is the point of scoring a coin that has a value of $10 for only $7 when you have to pay $5.95 for shipping?   Also, HOW do they ship them?  Do they just throw the coin in an envelope or does it come in a staple-over holder in a padded envelope?  Do they try to send it media mail, first class, or priority?
8. Combined shipping.  If you find a seller that seems to have good coins with good pictures, see if they combine shipping and are selling any other coins.  This is a great way to build your collection and to save money as well.  I'll avoid buying more than one item from sellers if they refuse to combine shipping, or do combine shipping but don't offer much of a discount for shipping charges.
9. Ask questions.  If you see an auction that interests you but you have any doubts, use the "Ask the Seller" feature on the auction page to ask the seller any questions you have.  You can usually get a pretty good vibe on how the seller is and about the item itself by the response you get.

Tips for selling coins:

1. Post pictures.  Take good pictures of your coins, both of the front and the back, and include them in your auction.  If the coin is valuable or of special interest, it might be wise to include a picture in the gallery.  People like to see what they are buying, especially when it comes to coins.  Even if the coin is in bad shape, take pictures and let someone judge for themself.  Even if its in bad shape, it might be an upgrade for someone else.
2. Include year and mint marks (and varieties if applicable).  This should go without saying, but include the year and mintmark in both your auction title and description, as well as any varieties (type 1, double die, D over S, etc).  Most collectors are looking for specific years and mints of coins, so this won't leave them guessing.
3. Be detailed in your description.  Are you selling just a penny, or a 1909-S Indian Head penny?  Is it an old nickel or an old 1937-D Indian Head Buffalo nickel?  Is it a Mercury Dime, or a 1916 Silver Mercury Dime?  The more keywords you can include in your title and description, the more hits you will get.  And the more hits you get, the more bids you'll get.  Don't try to grade the coin yourself, but you can list details about the coins appearance. 
4. Lots vs single coin auctions.  I generally sell more common coins in lots and the more expensive or 'key' coins individually.  Most people who are looking for lots of coins have a lot of holes to fill in their collections, which is what draws them to lots.  Once those holes are filled, they are looking to purchase individual coins (usually the pricier or key coins in the set) to complete their collection.  In most of my lot auctions, I try to avoid including duplicates as most people are only interested in obtaining one coin of a given year/mint.
5. Shipping charges/Combining shipping.  Clearly show your shipping charges in your auction.  Many people on eBay have been burnt by dishonest sellers who sell an item for $10 then try to charge $12.95 for first-class postage.  Because of this, people like to know the shipping charges up front.  Also, if you are listing more than one auction it's a good idea to offer to combine shipping for reduced shipping charges (usually something like most expensive shipping charge + a small addition for each additonal item won).  This will encourage people to look at your other auctions and possibly bid on them.  Finally, notate how you intend to package your item (box/peanuts, bubble envelope, etc) and what service you are going to use to send it (USPS first class, USPS Priority, UPS Next-Day, etc).
6. Start auctions prices out low.  I usually start all of my auctions at either 0.01 or 0.99.  There are a few benefits to this.  First off, the insertion fee is less.  Second off, it gets more people watching the auction (as opposed to those that are started at 9.99 or so), which can lead to bidding wars.  People are more likely to keep an eye on your auction if the price is started low than it is if it's started high.  I don't generally like to use Buy It Now with auctions for coins as values are different depending on which resourse one uses, and also because Buy It Now items cost more to list.  Let the bidders determine what the coin is worth to them.

I'll add tips to this as I run across them, but hopefully this is a good starting point!