This is so broad a question that I'm not sure if a comprehensive answer is possible.

How would I go about ensuring that my current game is running properly?

And by that I mean, that no scripts are there that shouldn't be, that there are no conflicts I haven't noticed yet, that sort of thing.

I use the wonderous and essential http://skyrim.nexusmods.com/mods/1840, in a basic way (still not sure what to do about the "suggestions" http://skyrim.nexusmods.com/mods/6 makes). But are there other tools? Other game elements to examine?

For instance, I am running into an issue in which Lydia won't follow me inside http://skyrim.nexusmods.com/mods/16028, which is a stunning mini-hideout mod. And I am using http://skyrim.nexusmods.com/mods/14037. I see people make comments that they
have examined various mod combinations and discovered this or that problem or red flag. So I suppose my question is, how would I go about doing that as well?
How would I take a long hard look at my current list of mods and my current saved games and troubleshoot them?

Any assistance offered would be greatly appreciated, thanks.