I know a lot of people tend to prefer cleanly polished IDEs, and I do use eclipse and eclim for java development, but normally IDEs tend to get in the way for me. As for the specific questions, building definitely isn't an issue and there are plenty of cross-platform build systems when it's needed. Continuous integration is usually handled separately on a build server (hudson, jenkins, team city, etc...). In fact, a lot of the collaborative tools for things like continuous integration and issue tracking are mostly usable via web applications (bugzilla, jira, etc...).
My biggest frustration is when tools that aren't usable on Linux get standardized on. Outlook is the easiest example, but for anything where it's absolutely necessary it's extremely easy to run a virtual machine with kvm and libvirt.