I just wanted to say that movie was awesome, but that there is a lot of adult humor in it, so I would recommend seeing it beofre you take your kids to ensure that the level is right for your kids. :P they drink mile like its alchohal...
Joy ride/steal a car
Death
But those were basically the worst ones .
Some other more subtle like stuff.
Have fun :P

For looking deeper, like you note, into movies, The US Conference of Catholic Bishops has a good movie review site. In their review of Barnyard, they say:

"Saving the film from being udder-ly disappointing is its admirable, if heavy-handed, message about embracing responsibility and putting the common good ahead of one's own self-interest. "A strong man stands up for himself. A stronger man stands up for others," Ben counsels Otis repeatedly.

The preachy and obvious manner in which it is conveyed works against the noble sentiment. Still, given our arrested-development age which celebrates extended adolescence and bemoans growing up, perhaps a little preaching is in order.

The film contains mildly crude humor, some menace and peril that may be upsetting to very young children, heedless theft and several mature story elements. The USCCB Office for Film & Broadcasting classification is A-II -- adults and adolescents. The Motion Picture Association of America rating is PG -- parental guidance suggested. Some material may not be suitable for children. "

Ty ima have to book mark that page.