What are the consequences of forgetting to claim priority to a prior filed application?

Despite the fact that 35 USC 120 states: "No application shall be entitled to the benefit of an earlier filed application under this section unless an amendment containing the specific reference to the earlier filed application is submitted at such time during the pendency of the application as required by the Director. The Director may consider the failure to submit such an amendment within that time period as a waiver of any benefit under this section"-- it nevertheless appears that a delayed benefits claim can be filed either by a petition for an unintentionally delayed claim (MPEP 1481.03) OR through reissue (MPEP 1402).  There doesn't appear to be any time restriction.

This is good news for patent applicants, but bad news for accused infringers.