There are so many consequences, some we don't know about yet with ads-on-jerseys. It all depends on if/when/how the NFL does this.
If done like stadium naming rights, there will be an arms race to attract the biggest sponsors. The sponsors that come to the Patriots will have deeper pockets than the Jaguars. Everybody will want a sponsor like Apple (except maybe Seattle.) In this scenerio, the rich get richer at the expense of small market teams.
The Steeler's logo is already an ad!
We already have seen how sponsors drop players if they get in trouble - this could get interesting. A team might want to drop a sponsor that becomes unpopular, maybe under fan pressure. Sponsors might drop a team for the same reasons, or simply to switch to a more popular team.