Upgrading a Specialized Sirrus 2015?
Yes, my friend just bought that bike new and ended up taking it back and getting a similar priced Cannondale, mainly because it came with a Shimano 105 group set. I would look at that as a major upgrade especially if you are experiencing poor shifting. If you have 500 to spend you could probably get an Ultegra group as an even better upgrade and have a really nice performing bike on your hands, as well as lighter. I'm not partial to Shimano so I'd probably check out Sram as well, Rival will be in your price range. 

A new wheel set would be the other major upgrade you could make for 500. There are a ton out there at that price but if shifting is what's bothering you I'd get that taken care of first.