I wouldn't deal with this by removing local admin privilege, that will do more harm than good, but I would recommend setting up a build server to verify builds in a controlled environment. The toolset I've adopted, which I've found works very well for me and my team of a dozen or so volunteers, is:
- JetBrains TeamCity - Continuous integration and build, plus unit test runner
- Atlassian Jira - issue tracking and project management
- Atlassian Fisheye/Crucible - code reviews and general code metrics.
- VisualSVN Server - source code control
- VisualSVN Client (integration with Visual Studio, well worth it).
- JetBrains ReSharper - programmer productivity and some neat unit test tools.
I can't recommend those tools highly enough. TeamCity deals with your "we found the bug after we shipped" by moving your builds off the developers machines and building in a clean, controlled environment. It'll also run unit tests and ensure that you always have a working build (by naming and shaming the build breaker).
Crucible is a valuable product that lets you do peer code reviews easily and with full auditing, so you can verify that they are being done correctly.
The other items I think are self-explanatory, they all contribute towards 'best practices' that will move your shop a long way up the 'Joel Test'. Atlassian has an offer for 10 licenses for $10 on some of their products, which is hard to beat.
All that notwithstanding, the solution to your development woes is going to be at least partly cultural. You can put these (or other) tools in place but you'll need buy-in from the team and management and you'll need to address your practices to ensure developers use them. Some re-education might be riquired, because sloppy developers don't usually like being forced to up their game. I would start with the build server and insist that no code can be released unless it comes from an automated build. A lot of good practices will fall out of that. You can consider adopting unit testing and code reviews as and when it suits your organization - but plan to do it from the outset.