I am not happy with my DS4054. Look here:
https://www.eevblog.com/forum/testgear/another-oscilloscope-thread-agilent-msox204a-vs-rigol-ds4024/msg932536/#msg932536
I wasn't happy with mine for the same reasons and bought a different DSO (MSOX4024A).
However, after reading a post about new firmware for the DS4000 series I updated the firmware. It was worse! The triggering was not working properly, as well as the issues that you described. It was almost unusable.
After playing with it I managed to get it to work properly, even the noise appeared somehow slightly less. It performed noticeably better than I remember it ever working.
What I did was run it though the calibration options that become available when you enter the secret key combination.
Try the following and see if it helps. You will need to get or put together a calibration cable, which connects all input channels to the calibration output on the back. Only perform the calibration after the DSO has warmed up, of course.
Enter the key sequence to enable the hidden calibration options.
Press [Trigger] Menu, then the following in quick succession, right soft key 7, 6, 7 then Utility key. (soft keys numbered 1 to 7 from top to bottom)
There should be a new option "Self-Cal" next to soft key 6. Run that.
If you scroll down (right menu down key) there will be an option next to soft key 7 called Project. Enter that then scroll down, there should be EqualCal and DelayCal. Run those too.
If you scroll down again there is also Probe-Cal which you can run, but I don't recall doing that one. On the same screen there is also an option called Default. I think that it reverts all the
options settings to factory default. I ran that after the firmware update too.
Hope it helps. It certainly made my DS4024/4054 usable again and I have put it back on the bench next to the MSOX4024A. I sometimes find the 14 graticule wide screen on the Rigol more useful than the Keysigt MSOX4024A, depending on what I'm doing, so often alternate between the two DSOs.