Yes, while there is nothing to freak out about, you have fallen into a Catch-22 that is probablly one of the biggest issue Americans have when immigrating to the UK.
They won't throw you out, but because you visa was not "validated" with a UK Entry Stamp, UKBA will likely argue with you in regards to when you started living in the UK. You essentially have no fixed date of entry in the UKs eyes. Yes, you didn't wander around Ireland for 6 months, but I am afraid that doesn't matter. When you apply for additional leave to remain in the UK when your current visa expires is when you might run into problems.
As other have said. The "best" way to fix it, is to leave the Common Travel Area (CTA, which includes the Republic of Ireland, the Channel Isles and the Isle of Man) and re-enter, passing through the UK Border to get a stamp. If this is near enough the time you entered, you are golden.
You could also plan now for a fight in the future, by again as others have said, by keeping as much paperwork the proves you entered on a particular day.
This is something Garry is leading on from an Advocacy front. You may get a message from him asking to share how you tried to get your passport stamped but couldn't. For some strange reason UKBA thinks we are being "sneaky" by entering the UK this way, when in fact it is simply a pratical situation of cheaper flights via Dublin.