I became a little confused as to what they were trying to do. I think it was something like this: they put some beacons on the ship, so they could jump a hundred+ times and use those beacons to somehow put together enough data to use to deduce a tracking algorithm for *any* (not just this) cloaked Klingon ship.
But then that didn't seem consistent with the action/sequences. Like in the scene Alteran linked to, why are they firing at it while doing these jumps? Wouldn't that be jeopardizing the mission if they accidentally destroyed it? Also, should it have been decloaked all that time as it appeared to have been? Felt like there were some inconsistencies, but maybe I just misunderstood, it was all a bit rushed on screen. TNG would have shown a nice discussion with diagrams before hand in the observation lounge, and I would have understood, lulz.
And then I also just had to wonder, how is it they can beam on and off so easily? Did I miss an explanation of this? I thought it was hard to beam onto a ship if their shields are up, did the Klingon ship not have shields? I know they beamed *on* sort of as they were de-cloaking, so that might explain why shields weren't up yet...but then what? Again I probably just got confused.
In my estimation Stamets seems to have gone Gary Mitchell after leaving the galaxy or some such. Ret-conning when/where man/one had or had not gone before....not a good canon look to be wearing...