There is no mention in the documentation about whether I have to claim ether before a particular date. Is there a time-limit on claiming ether? I've also heard that the mining algorithm will change at some point. Are my ether safe in the presale wallet, or do they have to be moved?
There is no time-limit to claim (i.e. import) your ether. Your ether can remain in your presale wallet indefinitely, and do not need to be claimed/imported until you are ready to use them.
Ethereum is, indeed, switching to a Proof of Stake consensus algorithm in the future, but here again there is no need to move your presale ether at that point.
As with all blockchain-based tokens, however, it is imperative that you keep your wallet (private keys) secure. Please ensure that you have backed up your presale wallet in a safe place (or two), and don't keep them on a computer that is (or can easily be) compromised. Also, please ensure that you know the password. You will need both the correct password and the wallet json file to import those ether in the future.
There is no time limit as the pre-sale wallet essentially is storing your private key. However, you might be better off converting to the current keystore format (the one used by
geth) in order to avoid any possible issue of finding a tool in the future which handles the pre-sale format. It is already getting problematic to use it (see other questions on this site about users experiencing compatibility issues).
The current keystore format became so widely used, that it is less likely to cause issues in the future. The encryption employed should be a tiny bit better as well.