I've felt that faux-texture phenomenon if I rub a finger on the stainless-steel surface of the dishwasher's door in the apartment I'm currently renting (living in a ~50-year-old flat I'm the Netherlands, though the dishwasher is almost brand-new). Would a similar cause of lack of grounding be at play here?
No clue what electrical in the Netherlands is supposed to look like but it sounds like it's a floating ground if you're sure you're feeling the same effect. Grab a voltmeter and check and if you're seeing 60-70V AC then it's probably EMI filtering. It's completely safe and doesn't present any kind of shock risk other than the fact that it's an indication that the chassis is ungrounded which means you don't have the added safety of shorting out the circuit if a live wire came loose inside and energized the chassis.
Personally I miss the days when protective earth was protective earth and you didn't have to worry about engineers doing foolish things like using it for EMI filtering or any sort of current path, even if miniscule. The safest class Y capacitor is the one that doesn't exist.
Until you get that looked into, I'd take extra care not to simultaneously touch the door with one hand and any possibly solid ground e.g. water pipe with the other.
Thanks for the suggestion. I realized something was amiss when I was placing a rinsed plate on the dishwasher and by accident touched the wet steel of the kitchen sink. I was lucky that it was only a small tingly shock. However, I've had trouble in convincing the landlady to fix it, since the contract stipulates that I need approval for any modifications.
Possibly, at least in my case the inside metallic parts in inside of dishwasher are directly (and by that I mean resistance is less than ohm) connected to ground.
Normally any leakage would be shorted to ground (and if too much and house has RCD, trigger protection), but if there is weak one, or none (some of the old houses even have only 2 wire install, with "ground" pin just connected to neutral)