Relying purely on freelancing to earn your bread can be somewhat risky and daunting. Say I want to do freelancing while also being employed (full or part time). What are the specific issues I need to keep in mind when doing this? What are the legal, time management, financial, etc ramifications?
Time management is an issue and you have to figure out how to meet with customers if working a standard schedule full time. The larger issues are legal. You want to read over your employment contract a few times looking at the specifics of:
Moonlighting clauses. When I worked at Microsoft, the contract said I had to have their permission to do any work outside Microsoft and that this permission needed to be renewed annually.
Non-disclosure agreements. Make absolutely sure that the domain you are freelancing is sufficiently removed from your formal employment that this is not an issue.
Non-compete agreements. Again, if you are freelancing in a different domain and not competing with your employer you are much safer than if you are working for your competition.
Depending on the specifics of your employment contract there may be other issues as well but these are the most common and serious.
I currently do exactly this, and while very dependant on your location, taxes can be a pain. I would recommend at least discussing things with an accountant
In the UK there have been alsorts of little bits and pieces I've needed help with as my permanent job's salary needs to be accounted for in my freelancing tax return as well as the tax I've already paid via the PAYE system.
Obviously these complications may be lesser (or worse) depending on where you are.
Other than than I really echo Chris' answer which you've accepted. Make sure your permanent contract doesn't hold any clauses that can catch you out.