https://play.google.com/store/apps/details?id=com.mxtech.videoplayer.ad
I recommend this over vlc at the moment. The nexus 7 2013 supports the hw+ decoder by the way so enable that. It will tell you about it when you launch the application the first time. It saves a ton of battery over software decoding.
I'm not sure that downloading an app excuses the fact that, out of the box, it won't play MPEG4 videos. Poor show.
Plus there's no file system like the S4. This Nexus 7 could be tonnes better but it seems Google are doing Apple's trick of making it a little bit useless and rather frustrating to use.
I didn't have these 'teething problems' with my S4, it all seemed to sort of make sense. I actually started to believe all the rubbish I read about Samsung, but I'm now realising Samsung have actually done quite a good job with Touch Wizz.