I've seen some sukkahs (especially ones where they've had big "make sukkah decorations" kids' projects) where there are tons and tons and tons of decorations hanging down from the schach. At what point would that invalidate the sukkah? Are there other decoration issues that are problematic?
Even if there's a decoration that completely covers the schach, if it's placed there merely for decoration, than it isn't a problem, provided that the decorations are within 4 tefachim of the schach (Gemara Sukka 10a, Shulchan Aruch O.C. 627:4)
However, this is assuming that they have been placed there for the purpose of decorations, otherwise, even a small object placed there for another reason (such as to catch leaves) would be a problem (ibid). This means that one (who needs to eat/sleep in a sukka) cannot sit underneath it, and it might make the whole sukkah invalid if it's too big (see daf 17 and the Shulchan Aruch 632). Most assume that this is true even if it is very close to the Sukkah (as implied by the Gemara on daf 10, though there are more details and conditions, see Mishnah Berura 627:14 and S.A. 629:19)
A lamp/light is considered a decoration and wouldn't invalidate the sukkah. In fact, the Chayei Adam writes that a person can even place a lamp lower than 4 tefachim from the schach if he does out of fear that otherwise the schach will catch fire, and the Mishnah Berurah agrees (627:19). I assume that the halakha would be the same regarding an electric lamp that could overheat and ignite the schach (but CYLOR, of course)