<p>Our application is written in ActionScript2 and has about 50.000+ lines of code. We want to port it to ActionScript3 and we're trying to find out what our options are. Do we have to do it manually or can we use a converter, and what problems can we expect? </p>

I don't think you can ever use an automatic converter for this task.
A converter may be able to save you some steps or point out places where change must take place, but you'll have to go over the code manually.
For example, referring to a _level0.variableName in AS2 can point to a movieClip on the _root level, to a FlashVar sent from the HTML container or to an object created by the code itself. There's no real way of knowing. (You can't look for the varname in the code since that too can be calculated or read externally.
You need to have a very good reason to do such conversion. If AS2 is not suitable anymore for some reason, maybe you should try to solve the problem instead of converting to AS3 just because it has a nice little function that you need.