Noticing that Tryndamere has issues actually using the moves Mocking Shout and Slash. Many times I'll go to use them and they go on cooldown, but aren't used. Not sure why this is happening either, but bringing it up in case it hasn't been issued. Has happened in multiple occassions, no real isolated incident for me.

I don't mean to question your diagnosis of the situation, but I have made the mistake of thinking the same exact thing you did, only to realize that mocking shout is not taken off cooldown unless you are in range of enemies either facing you or giving their back to you. But as soon as you get in range of enemies then the icon lights up (though its still grey colored and not very bright) and is usable. Give Trynd another go and see if you notice what I am talking about. The icon should be unclickable until you approach enemy champions, then it becomes clickable at least in my limited experience.