Samsung Galaxy S3 Internal Storage Issues?

My Samsung Galaxy S3 has a range of strange problems. I'm running CM11 but they started well before I moved away from Stock. I rommed my phone in hopes of fixing them, assuming it was software related.

Issues in order of appearance: - While recording videos with the camera, the picture will often lock up momentarily, then come good. This same stutter is then visible in the recorded video. Shooting video direct to an external SD did not fix this - When pressing the stop button to end a video recording, the camera interface locks up for up to a couple of minutes before I then see the slide out thumbnail to indicate that the video was saved to my storage. It seems the longer the video, the longer I wait. 10 seconds can take up to 30 seconds. Other times it can just be instant. - App store updates or installs fail occasionally for no apparent reason, but work on retry. - Screen suddenly goes blank, but the phone is still responsive. If I press the home or power button I get illumination on my buttons, as it does when responding to touch on the lockscreen. I've left my phone for up to 15 minutes to see if it comes good but sadly only a battery-pull does the trick. - Dialog box appears while receiving a call to say the Contacts has crashed.

I've been trying to find a way to scan for filesystem errors on my internal storage using fsck, but I can't seem to find exactly what I'm after. Surely there is a way to do a humble "check disk" on an Android device?