As I recall, that top plate didn't come in until very late TR6 (75-76). If it is late enough then your speedometer will be inaccurate after the swap. TR2-early TR6 all used the same drive ratio for the speedo cable (cable turns at 2/5 driveshaft speed), but that scheme was changed in 1973 to have the cable always turn at 1000 turns per mile. The difference is around 12%, meaning that with your speedo reading 65 mph (assuming it is accurate otherwise), you will actually be doing over 70.
I have a TR6 box in my TR3 (formerly in my TR3A). In addition to the changes noted above, I had to install longer studs, and then wound up trimming them to the exact length required. If they are too long, the tail flange fouls on the driveshaft tunnel during installation. (At least I think that was it, I don't recall exactly, just remember having to stop and cut the studs during the gearbox installation). I don't know of a source for the studs already cut to length, so you'll need to buy some threaded rod or longer studs and cut them yourself.
Possibly less than "minor" modification : the rear crossmember (plate that the rear motor mount bolts to) has to have new holes drilled to accommodate the extra length of the 4-sychro box. It's only about 3/8", but if you force it together without moving the holes, motor mount life will be much shorter. On my 3A, I then had to bend the flange at the rear of the crossmember so it would clear the motor mount.
The thicker flange moves the mounting position of the clutch slave closer to the lever. I had to make a shorter pushrod, the original didn't have enough adjustment.
I wound up also making a little tab to restore the length of the return spring. Without it, the clutch slave would sometimes stay partially extended, which put the clutch release point closer to the top of pedal travel. Not a serious problem at all, but I found it annoying, especially when trying to do a smooth start from a stop light.
There are some other minor differences, but they don't seem to hurt anything. TR6 input shaft is shorter, so doesn't engage as far into the pilot bearing. And the TR6 front cover is shorter, so might not support the throwout bearing carrier as well. Those have not been issues for me (but I am also running a TR4A-6 style clutch).
Oh, one last thing, you will likely notice that the first gear ratio is quite a bit 'taller'. That isn't necessarily a Bad Thing IMO, the TR3 has a "stump puller" 1st that isn't much use, but it is a difference.