Ah ha!
Truly brilliant puzzles.
I think the complaint that you can't tell what you can click on is unwarranted. Having the cursor change is a hint system that point-and-clicks don't necessarily need. In this game there just aren't that many potential things to click on so it's really no trouble to just try everything.
For the wire puzzle, you need to find the code in two parts. There is a set of symbols that appear in two places, and each symbol corresponds to a color. Look at the picture in the coat pocket to see what color each symbol is. Then look in the mirror to see which color connects to which, but remember that they're in a mirror!
You'll reveal what appears to be half of the box combination, but there's more there than just a letter and a number! There's also a symbol that is unmistakable as a chess piece. This draws attention to the fact that all the available letter-number combinations are coordinates on a chess board. If the indicated chess piece is at the indicated coordinates, what two possible spaces can it move to?
For the connect-the-dots puzzle, there's a pattern on a piece of toilet paper. Start with the dot at the number immediately following the given sequence, then continue the pattern. You'll form a symbol that kind of reminds me of a torch like the one the Statue of Liberty is holding. I have no idea what it's supposed to mean.
Also remember that hairpins make good lock picks and don't forget to check the dirt in the plant's pot.