but there is still the chance of sending coins to the wrong address or whatnot.
From my understanding, you use to be able to send coins straight to a public key1
(note: not a bitcoin address we all use today). The problem being that if you miss typed the key the coins are effectively lost, for it is near impossible to generate the private key from the public key. This is why the bitcoin addresses used today are in fact a hash of the public key with a checksum, so that miss types can be caught before the coins are sent. This causes each transaction to do the same hash on the public key(provided on the next spending of the coins) to check that the public key matches the address the coins were sent to (you can't go from address to public key, I think....).
But for all of these coins that are just "lost", are they really gone forever or can they be remined?
Cannot be remined. They will be "lost" until someone finds a private key that generates the public key the coins where sent to.
As people have said, only about 21M bitcoins will be mined in total. I assume that if a majority of the miners agree to change the protocol this could be changed, but don't quote me on it. IE instead of dropping down to 25 coins per block mined at the 210,000(?) block mark just continue giving 50 coins. The odds of this happen are rather slim, for one of the founding principles of bitcoin is the fair playing field. Of which knowing how many coins can be generated from the start is one of the key facts that make bitcoin a fair playing field (instead of having a central bank that can keep printing money indefinably for example).
And does that have any real effect on the economy?
I'm no economist, but if the supply goes down (from lost coins mentioned above) it stands to reason that the value of each coin goes up. By how much I have no idea. Another thing to consider: 50 new coins are minted about every 10 minutes, so currently, any "lost" coins in the supply can be replaced fairly quickly if the number of coins lost isn't a significantly higher magnitude above 50 (for example 1000 coins lost would take about 200 minutes to replace).
There is talk of a possible modification to bitcoin called demurrage that can bring back lost bitcoins by requiring all bitcoin to be moved within a period of time or become once again returned to the pool of unmined bitcoin blocks.
Sounds like a bad idea to me, how do you tell the difference between lost coins and coins in "cold storage" (for example bitcoins used for physical coins). What would prevent people from spending the coins that are thought to be lost after they are "added" back into the unmined pool? This would have the opportunity to increase the supply of coins past the 21M mark which would be bad for the reason given above. But hey, I'm just a noob ^^.
1: This is an assumption based on looking at early translations in the first 200 blocks or so. I only learned about bitcoin a couple months ago.