What is the best tweak?

Clean and treat ALL of your connections.

Power cords: Unplug from wall. Use a small fine toothed metal flat-file to file-flat both plug flanges (4 sides). Most plug flanges I've seen are stamped (by some kind of punch-press) and have a fine ridge, along the edge, that restricts contact with the female receptical (Seinfeld fans: "the holes").
File down until no more ridges and the blade surfaces are shiny and even.
Note: Some flanges have a raised bump running down the middle. DO NOT attempt to file the whole dang thing flat! Use common sense!
Next, use "Tarn-X" the deoxify the copper/brass plug flanges. This stuff can be found in most large super markets and makes metal look like new.
Finally, plug-and-unplug about 6 times to scrape off any oxidation from the female receptical. This is the best you can do until someone invents a $100 receptical that can be disassembled for cleaning (you can't expect this for a mere $50 dollars).

Speaker cable and ICs: Unplug and clean with alcohol first (the "non-sticky when dry" kind). Use your flat file on spade lugs where appropriate (forget it with those fancy Kimber kind). Again, you're trying to make the spade surface as flat as possible for maximum contact. use the file on amp connections and speaker terminals where appropriate (I don't have to tell you to unplug the amp first, do I?). Use your Tarn-X here too if connections are copper.
After filing and cleaning, apply something like "Pro Gold" or "Tweek" (follow directions) for maximum contact. For female RCA jacks (Jills?), pull most of the cotton from an ear swab and roll remaining cotton TIGHT! Dunk it in the non-sticky alcohol and "do" the inside of the jack.
Wait a while until all alcohol evaporates.
After all of this work (takes 2-3 hours) you'll be so tired that anything you play will sound fabulous!

Isolate your power cords. Be certain they are not touching any interconnect or speaker cable. Thats number 1 because until you do that, you cannot truly judge anything else.

Got to agree with Onhwy61. Positioning is number one. Consider all the angles of your speaker orientation, do they aim up down or straight ahead, toed in or straight, different heights if possible. Try them farther from and closer to the wall than you might think, especially if you have a sub. Position yourself, be aware of reflections from sides, back and coffee table especially where the sound travel path will have a difference of less than 5 ft. Try the differend phase switch positions on your sub. Then, in two months or so, you can worry about the things that cost money.

Dweller- you should also use you cleaning treatment on the main ground connection to your home. Clean and polish the ground wire, clamp and ground rod.

I use a high speed 3M buffing wheel mounted on a bench grinder to deal with AC connectors and spade lugs.

Kana813: The buffer will make the plug flanges look better but the flat file will make them uniformly flat for more contact. I've filed down many plugs that looked flat but had tiny hills and ridges on them. Good idea about the grounding rod. How often is this necessary?