Well.. as a relatively new owner also, I had the same issues...
For the gas mileage, I'd have to say it's because you're still within the engine break-in period and transmission learning. This will take about 1k-3k miles roughly...
The poor acceleration was an issue for me because the transmission needed an update to the firmware... they update the TCM at the dealership... this corrected the sloppy shifting/hard-hitting/ poor throttle response. This, of course, is assuming you have the 6 speed transmission and not the CVT. That's whole different topic for some of the older compass owners in this forum.
I also had the issue where , making a right on red, I had to put the pedal to the floor to get the thing to move, and even then it had a terrible drive by wire response... this all went away once I had the dealership update my TCM.
On a side note, you can boost the compass's performance a bit more with a K&N cold air intake and Magnaflow Payback exhaust system. Since I upgrade to this.. my gas mileage is better, throttle response is way better, and there's definitely more pep to the 0-60mph.
Lastly, how can anyone argue with the great sound it makes too!!
I have a 2014 compass 2.4l 6 speed automatic btw..
I hope this helps.