I'd wonder if they did that on purpose. Had you agree to the deal only to hook you in and 'bully' you to fork over an additional $1500.
There was another thread of a guy who underpaid (dealership mistake). But it sounds like he really underpaid (as opposed to not being able to see where the mistake was made). And his lawyer thinks it's an open and shut case because the contract was signed.
If you had overpaid instead, they would have said, "Too bad, so sad. It's a binding contract!" They sign contracts everyday; what are the chances this was missed by the arrogant manager?
If you can get the deal elsewhere, go elsewhere, and provide this feedback about the dealership's attitude to BMW NA.
2013 M3 coupe (Azurite Black, Black, Piano Black)
+ miata nut (2 miatas) + Mk6 GTI 5-door hatch (our mini-SUV