CiviPledge does allow recording of overdue payments

0. Navigate to a contact's Pledge tab
1. Create a new pledge. Set the first payment date to yesterday.
2. Expand the payment schedule.

Expect:

A link to record the first payment.

Result:

The first payment has no link. It can never be recorded. Even if I'm holding the check in my hand.

This is the simplest way to reproduce the problem, but it will also happen when a payment becomes overdue by virtue of time passing.

This is a pretty serious problem, as it can make it impossible to correctly record a given contribution. I would submit that recording complete and accurate information about contributions is paramount and overrides pretty much all other concerns. This is particularly critical to a back office deployment, as contributions are not necessarily recorded the moment they are received.

I reported this bug on the forums during the 2.1 beta and it appeared to have been fixed on the sandbox. It must have subsequently been reintroduced.