After updating the system to 2.7.2 I am no longer able to add or edit channel fields. I just get redirected to my default homepage and the form doesn't submit.
These types of issues are typically hard to pin-point, but I'd try two things first:
Re-download 2.7.2 and then replace your new 2.7.2 files/folders in case there was a corrupted or missing file in there somewhere. If that doesn't work...
After you've backed up everything up, start disabling fieldtypes one-by-one (and even extensions) to see if there's a third party culprit.