Is it safe to uninstall an old version of Bitcoin-qt after having installed the latest one? I´ve been using Bitcoin-qt (version 0.8.1.) for several weeks but lately I´ve had problems due to a so called "corrupted block database" issue, so I´ve decided to update my client to the latest version (0.8.5.). 

It´s already installed (I just installed it on my laptop without removing the older version), synchronized and working properly. 

Can I remove the older version of the client by clicking on the uninstall icon? 
Is it safe to do so? If so, do I have to backup my wallet.dat file again or the previous backup still works with the latest version?

Thanks in advance.
Since you don't mention the operating system, but talk about "clicking the uninstall icon" I am assuming that you are using Windows. 

Making a backup of your wallet.dat before updates and at regular intervals is sensible. If you installed bitcoin-qt 0.8.5 into the same directory as bitcoin-qt 0.8.1, uninstalling the older bitcoin-qt 0.8.1 might break your new install. If they are in separate install directories I would expect it to be alright (just based on what I would consider expected behaviour, I don't have intimate knowledge of the behaviour of the Bitcoin-QT-Windows client).

If you added any new addresses in since you imported the wallet to bitcoin-qt 0.8.5 you might have generated them after the last backup, so it would be prudent to create an additional backup of the newest wallet.dat.

Usually, I'd consider the following the correct order for an update (unless the software has its own update function):


backup
uninstall old
install new
import backup (by keeping the backup alive!)