I've noticed that sometimes after I've mined a mineral, it causes a sprint glitch in first person mode. It basically stops sprinting alltogether apart from a quick lunge forward after pressing the sprint key and then it returns back to normal running. However in 3rd person mode, which I hate using, it works fine. It only affects first person view.

I have no idea whether it stops happening or how long it can last for as I have always reloaded my last save after it happens.

I get this if I'm in stealth/crouch mode when I started mining.

It sometimes does this if you go straight from sneaking to an activity such as smithing, cooking and enchanting. Just go into sneak mode, then come out again.

It could be that too, but I'm pretty sure I've actually noticed it happening without sneaking. Once I've made sure the coast is clear and safe to stand normally, I do so, then I go back and mine the minerals. Plus when I'm travelling on foot from loaction to location in the wilderness, which I do a lot instead of fast travel, I only use sneak if I'm stalking an enemy. Apart from that I'm running and sprinting through the wilderness and stopping to hack at the occasional ore vein I find. It's happened then as well... Unless I've accidently hit the sneak button on those occasions and not realised.

Having this same problem but I can't then get out of sneak mode. The sneak symbol isn't up by my character is permanently stuck in a crouch - pressing the sneak button does nothing.
It only seems to happen when the minning interrupts itself without tapping the seam of ore.