Would the new 677 Mhz ram mixed with 800 mhz ram have any problems with my pc?
Well, RAM from a diff. batch might cause some errors even if they are of the same manufacturer/latency/frequency & capacity.
I know both the rams wont run at their maximum capability but still would the difference be that BIG?
Nah, the difference would be negligible.
Also I would still be benefited by 4 GB of ram than 2GB even if their clock speeds are different right?
Yes, you will benefit from 4gb. A 64bit OS (with 64bit apps)would make better use of that 4gigs.
Its not really a good idea to mix different speed RAM, but it might just work for you.
Run Memtest86 to test your RAM.(If you choose to go through with it)