What types of error messages would I recieve if the backbone of the network is setup for both Unix and Windows systems?
Your question is vague in the extreme. In general you won't see anything specifically due to this configuration. Is there a specific problem you are having?
Honestly I would try a web search engine. You might find an answer there.
"Even a blind squirrel finds a nut every once in a while!!!" 
Error messages about what?
More information is needed! Or as stated before use a search engine.
(sounds like homework to me)
You would get error messages related to both open TCP/IP protocols and Microsoft networking protocols.
Out of curiosity, I had a look at the logs on couple of routers (Cisco & Extreme BD) here, and I don't see anything specific to the network being mixed, and have to say I have never seen any problems with this configuration.
The question I have is what level are you talking about error messages? Are you talking about errors in layers 2,3 or 4 communication? or at the end user teminal?
The one unrelated thing I did notice in my configurationwas that the ARP cache in one of the routers is too small. I'll sort that out tomorrow, when I have a scheduled downtime. I know it's OT for this thread, but it's one of those things I'd have overlooked if I hadn't been prompted to look.
I've never seen a network setup specifically for either Windows or Unix or for both --- if there are any errors to be seen --- most errors will be normal TCP/IP-related errors that will be applicable to both platforms ... Microsoft networking protocols will add some errors but so will any network-aware applications running on either platform ...