Admittedly, these are caused when the user doesn't know what he's doing, but they shouldn't really occur anyway.
No bug should ever occur, even if the user "doesn't know what he is doing" :) Thanks for reporting these, both bugs confirmed and will be fixed for the next release.
If you don't declare a variable, all instances of that variable throughout the code appears in red. What about each project having a list of words which the syntax will assume as valid? As a user, I'd like to take my cursor to the position of the variable, right-click and select an option (e.g. "Treat variable as valid").
Too many problems can arise from this - How to treat that word, what color to use for highlighting it, what if you later declare a variable with that name, where to save that list of words etc.
I presume that you already know that you can turn Strict mode off, but you want to use Strict mode and find it tedious to now declare all the old variables that aren't declared ?
If that is the case, what about a command "Add declaration for this word " that will add a declaration for a local or global variable at the beginning of a function / file ?