After the blooms have finished you have 2 choices, cut the bloom stalk off right near the plant and let the plant rest, or cut the bloom stalk between the points of the first blossom and the first node below the old blossom. It looks like a very vigorous plant, and would very probably branch, but if you cut the stalk off completely you will get a much better show next blooming.Originally Posted by PyroRob
The leaf tips seem okay to me. I suggest leaving them alone, as trimming them can open them up to infections.
The mosiac pattern looks like sunburn to me. Keep an eye on it, but I don't think you have anything to worry about.
Cleaning the leaves - I have heard lots of different suggestions (milk, sun oil, etc.) I just try to wipe mine down with water on a paper towel once a month.