1. Remove your fenders and throw them away, or you will die.
2. Upgrade the generic 415 chinese chain with heavy duty #41 chain. This is less of a "if you do this you'll get by" thing, and more of a required upgrade. Aside from having much higher tensile strength, the extra width of the #41 chain will allow for some side-to-side sprocket wobble. If there is wobble while using 415 chain, it will break into pieces overtime.
Farmex/Speeco 06411 #41 Roller Chain
This is enough for two full lengths of chain with a little bit of leftover.
3. Buy extra master-links, since they are the weakest link in the chain. I've broken two master links so far, one of which was directly my fault. You should carry these around with you.
Farmex/Speeco 66411 Roller Chain Connecting Link Pk/4
5. You will need a chain breaker to break the chain down to size. Do not skip this. You will not be able to break this beefy #41 chain with anything else.
Tusk Chain Breaker | Rocky Mountain ATV/MC
4. Replace all of the crappy low-grade 4.8 grade bolts with high-grade 8.8 or higher metric bolts. This is best done at a local Home Depot or Menards rather than over the internet. Buy a couple extra incase the bolts do somehow snap.
5. Replace all of the supplied nuts with nylon lock-nuts.
6. Buy a bottle of blue 242 loctite. Use it wherever you can.
6. Buy yourself some sort of fuel filter, I use this one. When I was changing my fuel line out a few weeks ago, I shook this around and you could hear a BUNCH of little tiny what appears to be rocks or something. This will keep crap out of your engine.
ROTARY PART#20-6000 FUEL FILTER FOR BRIGGS & STRATTON - eBay (item 310235550256 end time Oct-19-10 02:21:51 PDT)
Also since you just got your engine, I would recommend you break the engine in with non-synthetic oil first, then upgrade to fully synthetic Amsoil Saber at a 50:1 ratio. Or for added protection (But more work) run it with 2 ounces of Amsoil Saber and 0.5 ounces of Marvel Mystery Oil per gallon.
As far as keeping an eye on anything, that would be your chain tensioner. I've read stories about people throwing their tensioners into their spokes and stuff, but it's never happened to me. I simply replaced the crappy hardware with higher grade bolts and double nutted everything. I've never had a single problem. People will try to convince you to fabricate a make-shift tensioner out of a rollerskate wheel and stuff like that, but that's entirely up to you. I've tried running a straight chain multiple times, but I never could get it to work with my 44 tooth sprocket.
This is the most basic stuff in regards to the engine and the kit. Then of course, there's the bicycle itself.