For the sake of information...
"Data Error (Cyclic Redundancy Check)"This means a file failed the torrent hash check, indicating the file is corrupted. Usually you can resume these and redownload the bad piece after the check is complete.
"Invalid download state, try resuming"This can indicate two things;
1. One (or more) of the files in the torrent has been moved, renamed, modified, etc. This usually happens with seeding torrents. In the first two cases, a good client will allow you to "find" the missing file. As long as it hasn't been modified, you will probably be able to resume without re-checking. If it was modified, you're pretty much SOL- you'll have to redownload it.
2. Your computer crashed/power went out while a file was active. This only happens when downloading. Since the file was being written to when the client unexpectedly quit, the data won't match up with the client log, since the log is not written until a chunk is completed. It's like if someone went to a construction site and finished building a wall overnight- when the bricklayer comes back, he'll be confused and want to check everything to make sure it's okay.
I only got the CRC error once, but after looking up what it means, it kinda makes me paranoid since it could mean I have bad sectors on my HDD or something... Then again, it could also just mean I restarted while the torrent was downloading. I haven't seen it again, so should I worry about it?
Unless it starts happening a lot, it's not something to worry much about.
I only have one other one that has some sort've weird thing... But it just has a red up arrow and says it's seeding, but there's nobody connected [0(1) seeds, 0(0) peers].That means the tracker is down/unable to connect. (It sounds like you're using uTorrent?) If you go to the tracker tab, it'll have a status message. If it says 'offline/timed out', then the server is probably down for maintenance. If it says 'not registered with this tracker', then the torrent has been swapped or removed. You should get a PM in those cases.