If I see an unconfirmed incoming transaction on my Bitcoin Client, and those bitcoins are later spent elsewhere, does the incoming transaction disappear without a trace from my transaction list?
Yup, unless you were somehow able to do a spend transaction with those funds (e.g., from another client that allows spend using unconfirmed funds)
Does it disappear from Blockchain.info records?
Not right away, I believe the double spend transaction will persist for about a day or so.
Speaking of which, can Blockchain.info wallets be used for double spending, or do you need custom software?
It isn't the transaction that you know about that will look anything different. It is the second, double-spend transaction that gets mined and included in a block that becomes the problem.
Is there any "safe" time during which a double spend is unlikely to happen?
Nope, until a transaction has a confirmation any miner can include a double spend transaction that the rest of the network doesn't know about (or has rejected).
Any other signs that I should keep an eye out for?
There are some rules that can be applied to filter out transactions that will likely get mined in the next block (sent using only coins that have already confirmed more than a day ago, transaction below 10K in size, and a fee was paid.) versus those which will not get mined anytime soon (any of the folowing ... larger than 10K, no fee or inadequate fee, includes an input that itself hasn't confirmed, lots of "spam/dust" transactions, etc.).
Accepting 0/unconfirmed transactions will be like an arms race. You can tweak some things on your end, and the attacker will try to game it. You simply need to make sure it is not economically beneficial for the attacker to keep trying and the problem will be minimized.
