TeamStat.Score should be an int, but the API currently returns an unsigned int. The HaloEzAPI wrapper model has the property as an int, so when an unsigned int that's too large for an int comes through, it explodes.
There's a bug, but whose?
On one hand, the API shouldn't be returning an unsigned int because score can be negative. On the other, the API currently does return an unsigned in, so the model should represent this.

https://github.com/glitch100/Halo-API/blob/master/HaloEzAPI/Model/Response/Stats/TeamStat.cs#L8
vs.

https://github.com/gitFurious/HaloSharp/blob/master/Source/HaloSharp/Model/Stats/CarnageReport/Common/TeamStat.cs#L12

Everytime I try to initialize HaloAPIService I get an object reference not set to an instance of an object error

The MedalType enum errors out as there is no type set for new types i.e ball

https://github.com/glitch100/Halo-API/blob/master/HaloEzAPI/Limits/RequestRateHttpClient.cs#L85

If Stopwatch.Elapsed.Seconds >= SecondsLimit than the following equation '(SecondsLimit - seconds) * 1000' results in a negative number. i.e. (10 - 11) * 1000 = -1000.
You can't sleep for a negative amount of time.

Looks similar to issue #2.

GET /stats/h5/arena/matches/c44a03be-36c3-4327-8946-7dab19e91c1d HTTP/1.1

Additional information: JSON integer 4248941445 is too large or small for an Int32. Path 'PlayerStats[4].MetaCommendationDeltas[0].PreviousMetRequirements[0].Data1', line 1, position 16559.

Sure enough, all of those values are very large. Not sure what the data type should be, but almost certainly not an Int32 :)