Due to bug 720346 there may still be some updating issues when trying to update from Thunderbird 10.0.0esr to the newly released Thunderbird 10.0.1esr. This bug does NOT affect the regular desktop versions of Thunderbird 10.0.0. No word yet when this may be fixed. If needed users can manually download and install Thunderbird 10.0.1esr here. The next scheduled update for Thunderbird 10.0esr will be Thunderbird 10.0.2esr on March 13th.
While on the subject of version numbers, Mozilla in an attempt to fix one issue has once again caused (or recreated) another issue. We are back to the version numbering getting all wonky when there is Chemspill or Firedrill releases. With Rapid Release we know that on March 13th, the next regular release will be Thunderbird 11, regardless if there are any more emergency releases between now and then. With Thunderbird ESR, version 10.0.1esr was suppose to on March 13th, but now with the emergency release last week the next version will be 10.0.2esr (as long as there are no other releases between now and then). This just adds to the confusion as to which version is current as we have seen with the soon to be retired Thunderbird 3.1.x branch.
UPDATED: This issue appears to be resolved now and users are moving over to Thunderbird 10.0.1 ESR via automated updates.