If two people try to access the same MXD on the company server, only the first user to open the MXD has the right to save any changes -- the second user will receive a Save error without knowing why (either the network connection failed or someone else has it open & active).
Would be helpful to either see a physical "lock" file similar to that of shapefiles, but on the MXD itself -- that would be an immediate notification before trying to launch the file from Windows Explorer. In the instance that a user would attempt to open via ArcMap (and not see the "lock" file in Windows Explorer), then a notification should pop-up similar to Microsoft programs, i.e. "[User A] has this MXD open for editing. Would you like to A) be notified when available for editing, B) open read-only, or C) cancel?"