I'd like to develop an open source web application. Are there special security concerns which are introduced by the source code being open, in addition to the usual ones which apply to closed-source web applications?
Not really, no.
OK, I'll expand on that ;)
The only difference between open source and closed source is the fact that its easier for everyone to see the source code for open source app. Note that I said easier. There are plenty of examples of closed source code being 'stolen' or leaked.
When you implement an application you should assume that any attackers have access to the source code - that way you hopefully wont rely on 'security through obscurity' (a bad thing).