'81 KZ650 CSR - Head Rubber plugs

Yup - I probably went way overboard on carb maintenance than I needed to, but thankful that I have now! Along with new oil, oil filter, air filter, and spark plugs.
It was close to 9pm when I got it running last evening, and our one neighbour has two young kids, so I did not want to run it too much. So I hope to one evening this week or this weekend to put the air filter in, dump in some Seafoam, and then let the engine run for a good 30-minutes. I think it has been at least a year since it has run. 

Yes - on to the other areas of maintenance. I did notice that the clutch did not feel 100%, so I'm going to make sure that the clutch is adjusted properly.

Also need to get a working headlamp, taillight, and turn signals!

You didn’t mention brakes. Very critical. The last thing you want is the joy of having it running turn it despair at the end of the block when it won’t stop. 

Brakes are certainly on the list! 
Based on the tire-wear difference between the two tires (the back one is worn a lot more than the front one), I wonder if the kid who had it before me did lots of burn-outs to impress his buddies. So I want to make sure the brakes are safe.

Take that as a good sign. The bike had to run well enough to do the burnouts.

Keep the forum posted. Enjoy the bike. 

If you plan to run the engine for thirty minutes without the bike moving, I think it would be a good idea to have a large fan blowing on the engine to prevent overheating. Air cooled engines do not cool well when stationary.

What's a good length of time to run the bike for to help clean all the old stuff out? I honestly just pulled the "30-minutes" number out of thin air!

How bad was the old oil & oil filter?  You could use that as a guide as to whether or not the engine needs special treatment.  It normally takes about 20 mins to fully warm up the engine when not riding.  However long you choose, as TexasKZ said, be sure to run a fan.  I use two small tilt fans, especially to keep the header pipes from turning blue. my exhaust system is in excellent condition.  As for the rear tire wear, that's fairly normal on a motorcycle.  For the headlight there are a number of options.  I installed an H4 headlight from an 82 KZ750 Ltd >> it was a direct swap.  I just needed the lens unit, H4 bulb & dust cover.  The halogen headlight is much brighter than the old dim sealed beam unit it replaced.  but there are probably brighter options available.  Be sure to adjust the clutch properly as listed in the OM or FSM.  It's kind of counter-intuitive.

The oil was certainly dark but I don't recall anything being alarming about it.
Twenty minutes seems like a reasonable amount of time. I'll be sure to grab some fans to keep 'er cool!
Good to know about the rear tire wear. 
Yes - now that I know the bike runs, I'm shopping for parts so that I can more safely take it on the road.

Rear brake.  assuming you have no idea how old they are.  No matter their condition, replace the rear brake shoes.  The adhesive that binds the linings to the shoes becomes brittle over time, so a lining can separate then get jammed between a shoe & drum, locking the rear wheel.  It happened to me, so it does happen.  I hadn't examined them beforehand, but except for the one lining that came off they looked fine & there was plenty of braking material left. so you can't tell by looking at them.  Don't breathe the dust as it may have asbestos.
Front brake.  Old old old brake lines can burst, but I've never seen that. It's rarely mentioned so not sure how common that is.  Original brake lines would be way overdue for replacement.  I think the manual says every 6 yrs or something like that.