So, the government has spent $111,600 and have the application in hand. Now they have to pay a reliable company to field test the application, accept or reject it as meeting the original specification, and if they accept it, to train the the trainers in how to use it. Considering all the presentation and training material that will be generated, that's probably going to cost about $100,000 but can be limited by limiting the number of trainers that are initially trained.
Someone will probably get a bonus for keeping the total delivered price below $250,000 which would have put it into a different category and would have driven the cost up even further. Now as for it not working and the interface being crap, that's not an issue unless the specification required that it work and the interface not be crap. If the friendly professor they hired hadn't specified software much there's a good chance that no such specific requirement was included. Live and learn, of course, and after specifying a few he'll get the hang of it and be an even friendlier professor as well. Those agencies that really care about getting quality software the first time pay friendly professors who have retired from the agency that is seeking the software product. In this case, someone figured it was so trivial they'd let a new guy have a shot and you saw the result.
Regards
Local government is just as idiotic. I worked for a major city's IT department. The police department contracted a private firm to create software for laptops in their police cars, at a cost of hundreds of thousands. I went through their training course alongside police officers, as a liaison to the police from the IT department. It was a piece of crap, and it took me five minutes on a police laptop to bypass it's security and corrupt the server and take administrative control. Not a good thing for protection of criminal databases. Needless to say, I embarassed them.