First, make sure that you and your coauthors use the same TeX distribution. Suppose your co-authors use some form of Windows: if your main computer is a *nix machine and you use TeXLive, then try hard to get your coauthors to use TeXLive for Windows.
Second, make sure that everyone is using the same vintages of all latex packages.
Third, make sure your co-authors use a text editor that's reasonably TeX-aware. Put differently, if they use Windows, do try very hard to discourage them from using notepad.
Fourth, and this is not so much a matter of somebody being more (you) or less (your coauthors) TeX-savvy, but a matter of sound resource management: use some kind of version control software and find a way that everyone has equal and instantaneous access to all files, be this via a shared dropbox folder, a github account, or whatnot.
Fifth, especially if your coauthors are new to LaTeX, do yourself a favor by cleaning up your LaTeX code thoroughly before you let them see it: consider removing all deadwood code, not loading unneeded packages, providing lots of comments and whitespace in the LaTeX code (never a bad habit anyway, right?!), and providing some reasonably self-explanatory templates for items such as tables and figures.
Next, if you've written some specialized macros, make it reasonably easy for the co-authors to access them, e.g., with a keywords interface, and provide some kind of input sanity checking so that the improper setting of a parameter doesn't cause crashes followed by much gnashing of teeth. Don't expect things to go well with your co-authors if your macros take more than three inputs. If your macros are buggy and require sifting through TeX's cryptic error messages, don't inflict them on your coauthors unless you want to terminate some relationships for good.
Last but not least, give them (i) a list of URLs to the online user guides of all important LaTeX packages you're going to be using and (ii) both a hardcopy of and a link to Tobi Oetiker's Not So Short Introduction to LaTeX2e. And, be sure to point them to these documents repeatedly, whenever they get confused, irritated, or both.
Happy TeXing!
mathtoolsrequires theamsmathpackage, you needn't load the latter package separately, do you? And, instead of\newcommand{\bvec}{\mathbf}, consider using arguments explicitly, as in\newcommand{\bvec}[1]{\mathbf{#1}}. All these little things will add up in terms of establish LaTeX cred with your coauthors. :-) – Mico Dec 9 '11 at 23:17