Second thing you should consider is what software you use to convert the video into mp3. There are a lot of free software that do the job (a few are really good), but for some of them you have to pay. If the second case the problems will appear when you use cracks or key generator for the license code you may have problems. The immediate problems are the viruses and malwares that usually come along the key generators (the executables are often infected with them), the long time problems are the legal ones. The software developers know about the methods to avoid paying for licence and they are creating new methods to catch you in the act - one way or another they'll get you.
Probably the best way to download videos and convert them to mp3 is to use several softwares in the same time. The number is limited only by your desire and the software requirements (your computer may not be good enough for some software), but you should use more then one. Consider that some of the videos may not be accessibles with one software (considering you are using the same tool to download and convert) but they will be downloaded by the other one.
You should also consider that Google always updates the scripts and algorithms on youtube. Some of the modification will not be observed by the end users, but they happen. The big updates will change the user interface and/or the way to access the videos. It may happen (as it did happen before) that in one moment of time you are able to download any video you want and in the next moment you can download nothing. So use the download and convert softwares that are being updated as youtube is updated.
There are some online services that can convert youtube videos to mp3, but always check the quality of the files before consider the job done. The online services depends of your bandwith and the load of the server. When the server is overloaded with its jobs it may have bad results, including your mp3 converter.
The last thing I want to tell is to always keep youself informed about the news. The things always change, including in the legal world over the interned, new and improved download software and script and mp3 converters appear every year. Update your antivirus often
