Ya, I have that problem with the guy in seyda neen all the time when trying out new mods. It happens because whoever made the mod didin't do a good job of testing it, they mess with stuff that affects the main quest and don't realize it. The only way to fix it is to load the mod in the construction set and do it yourself or let the author know and they might post a new version. I'm assuming you get most of your mods from planetelderscrolls?
And its not just with main quest characters, lots of other things can be messed up too. Really annoying to play a new character for several hours and then find that creeper no longer buys or sells!
As far as DDE's go: xbox only has 64mb of ram, so take a look at how big the mods are before you ftp and install them, some of them are just too big

. When you save games always make a new save, don't save over old ones, never leave doors open if you can help it, don't leave tons of stuff lying around; every container you open will add to the info the game must keep track of and when you've got hours and hours into it the save game files get huge and dde's can happen just from that too.
One thing that can make a huge difference is resizing the textures in a mod. If you're handy with a graphix program you can significantly reduce the memory usage of a mod just from doing this. Haven't done it myself. Seems like it would be really time consuming. I don't know in what order the xbox loads the mods, I'm assuming alphabetical, but you might try renaming mods to change load order (I know on pc the order you load the mods can make a huge difference).
Also, mods that have heavy scripting will give problems, and ones that require MWSE just won't work.