Does everything need to come to code
Fat aluminum can stay put

Aluminum was only a problem when thin, solid aluminum wires made from the wrong alloy were rushed into branch-circuit service hastily in response to copper shortages.  Fat aluminum wire such as that used for stove and electric-furnace circuits and feeders to subpanels never had such problems, and is quite safe due to the aluminum-alloy screw-lug terminations used with it (vs steel screws and sprung wirenuts).  Furthermore, aluminum wire made since the 70s uses a different alloy that doesn't have the same problems the old, bad stuff did -- this new alloy (AA-8000 series, as it's called) is Code-legal for brand-new work, even.  If some insurance or lending type tries to tell you to rip those fat aluminum wires out "or else", tell them to go read 310.106(B), or ask them what service wires are made from for that matter.

Your panel is 99% fine...until you consider the location

Your panel, while slightly odd (it's a "split bus" or "rule of six" panel as per 230.71(A)'s "two to six disconnecting means" rule), isn't a Code issue by itself save for the double tapped lug, which can be fixed with a pigtail and wirenut as Harper describes (if anyone says you can't do that, tell them to go re-read 312.8).

I can't tell what the weird thing with the LEDs in it is (it might be a whole-house surge suppressor) as I'd need a much clearer photo to see the labeling on it.  Don't worry about it for now, though, as you have much bigger fish to fry: either the idiot who installed your panel put it in a clothes closet, or some other idiot came by and put a clothes closet around the panel later.  Not only does it look like the location violates the 110.26(A) clear working space requirement of 30" side-to-side even if that space is offset, annoying your electrician to no end, this panel was placed in a spot that's a blatant fire hazard.  Overcurrent devices or even panelboards themselves can fail quite spectacularly when pushed beyond their limits, and Code takes this into account in 240.24(D):


  (D) Not in Vicinity of Easily Ignitible Material. Overcurrent devices shall not be located in the vicinity of easily
  ignitible material, such as in clothes closets.


So, either the clothes (and the closet fixtures such as the hanger rod) have to go and stay gone, or the panel has to move, otherwise this installation will get a nice, fat write-up from the electrical inspector no matter what else you do.