Hi all!
Thanks for all suggestions. It turned out to be dodgy connection on the voltage feedback resitor divider. All measurements were OK, but today I just blew off both resistors with hot air to check them separately, then soldered both of them back and it works. Shame on me.

I cannot see the 220uF output capacitor and possibly only one of the 1uF on the output in the layout overview. The datasheet mentions low ESR type capacitors, so those capacitors should be located somewhere close. During the fast switching it might be possible that the regulator only sees the 1uF ceramic capacitor and that voltage is also used for the feedback.
Yup, the layout without designators look confusing, the guy on the TI forum didn't find the output cap as well. I've attached the version with designators shown.
Regarding the ceramics on the output, strangely enough, TI design tool (WEBENCH) just recommends a single low ESR tantalum cap on the output - I've added 1 uF MLCCs myself.
The output cap is as close as possible to the V sense feedback exactly as you've suggested - the middle point of resistor divider connects right to the cap pin.
Actually, this Panasonic cap raises some questions. They state 35 mOhm max ESR@100 kHz in the datasheet for 6.3V 220 uF
This value, if put into the formula from the TPS5430 datesheet gives me perfect 18 mV output ripple voltage. However, the measured ESR on those caps I have is more like 120-130 mOhm, which gives much less enjoyable 60 mV ripple, which is exactly what I see in the scope trace. Any ideas why?Ok, that's me being an idiot, noise was picked up by scope ground wire, measured with the proper probe (with spring clip) and now it's well within 20 mV.
And another question - can someone explain the PWM shape under small loads? I've attached three traces:
12V input, 5V output, 50 mA load
12V input, 5V output, 1.6A load
24V input, 5V output, 1.6 A load
The latter two look perfectly reasonable & the duty cycle changes according to the change in input voltage.
The trace under 50 mA load looks like a strange overlap of the normal rectangular wave with some half-arsed half-sine. Has anyone seen anything like that?