I installed the mesa drivers from nonfree.eu to get gpu vaapi with my old HD4250 radeon graphic.
That is working good only with videos up to 1280/720 resolution.
If I play videos in 1920/1080 resolution I’m getting very slow/stuttering Videos with Audio/Video desynchronisation detected message:
Is my video hardware simply too slow/old for playing full HD?
Are there any special settings in mpv that could help?
?
We know nothing about your hardware. 
https://nonfree.eu/
for getting h264 support
As I wrote in the first line of my post: Radeon HD4250 Graphic
I can also reproduce the stuttering, though not the status error messages:
$ mpv --hwdec=auto Downloads/drone_footage_of_high_rises_in_a_city\ \(2160p\).mp4
(+) Video --vid=1 (*) (h264 3840x2160 23.976fps)
Cannot load libcuda.so.1
Using hardware decoding (vaapi).
VO: [gpu] 3840x2160 vaapi[nv12]
(Paused) V: 00:00:12 / 00:00:43 (28%) Dropped: 46
Exiting... (Quit)
Interestingly my settings produce less dropped frames counted … but roughly the same experience:
$ mpv Downloads/drone_footage_of_high_rises_in_a_city\ \(2160p\).mp4
(+) Video --vid=1 (*) (h264 3840x2160 23.976fps)
Using hardware decoding (vaapi-copy).
VO: [gpu] 3840x2160 nv12
V: 00:00:13 / 00:00:43 (31%) Dropped: 3
Still more interesting is that the same video in smpayer (set to use mpv with the same settings) produces normal playback.