What would be more modern way to do this? Maybe some sort of chemical sticker (reacting with oxygen) on the window?
A valve included in door (or wall) design
The simplest way to do this would be to have a cylindrical hole drilled through the door or through the wall next to the door, with a valve in it: in section:
| +----------------------+ |
| | +-----+ | |
+-----------+ | | +---------+
+-----------+ | | +---------+
| | +--X--+ | |
| +---Z-------X-----Z----+ |
| interlock: when the two X's are |
| aligned, the door can be opened |
You can have a spring mounted inside the chamber. If the pressure is equal on both sides, even in the dark, even with shipsuit gloves, even in microgravity, you'll still be able to move the valve end in and out slightly and feel it moving. If there's vacuum or overpressure on the other side, the valve will disappear inside or remain stuck outside, and chances are you won't be able to have it budge easily; again, this will be immediately apparent.
Additionally, the valve ending could be shaped as a whistle, so that forcing it open would cause a piercing whistle to be heard. And the valve might be made large enough that forcing it open on purpose (which would, at that point, require considerable strength) would exhaust the atmosphere in a reasonable time. This is because you might happen to be trapped in a pressurised room, with your suit on, the power off, and unable to exit because you can't open the door against the pressure. Opening the valve would depressurise the room, freeing the door and allowing you to reach the escape pod or whatever (in a similar way, if you ever find yourself in a submerged car, you won't be able to open the doors against the pressure until the car is full of water, which might require opening the windows).
You could also have, instead, a transparent window with two aneroid barometers at both ends, or devices such as a small sphere full of helium gas inside a pierced cylinder - it will float upwards in atmosphere, stay down in vacuum. But this kind of check looks more complicated and error-prone to me; in the case of the helium plunger, as Lenne observed, its operation also depends on there being gravity.
One advantage of the mechanical nipple sticking out or being drawn in is that it can be easily used to both electrically and mechanically override the door lock, preventing it from opening unless pressure is equalized. Then you'd need an override to the override, but that's engineering for you.
Fancier but less robust design
Same as above, but now the plunger (which will probably need to be larger) is also connected to a moving arm or gear, rotating a circular sign disk inside an armored glass window - sort of those toilette signs saying "OCCUPIED". The sign would be divided in three equal slices saying 'PRESSURE', 'NORMAL' and 'VACUUM' on both sides, with the two faces mirrors of one another and aligned on 'NORMAL'. Only one third of the circle would be visible through the window, and normally it would read NORMAL on both sides when the plunger is in the middle (you get the idea).
Emergency tests (for doors with no vacuum check valve)
So you're left in front of this door which you want to open to go on, but - what if there's no air on the other side? The door is not equipped with the valve described above. What can one do?
Door structure: check that the door is not bulging inwards or outwards. If it is not, chances are that it's too thick and rigid for Heikki Mäenpää's "knock test" to be conclusive, but -- try knocking all the same.
Noises: hisses would be strong indicators of a significant pressure differential (and an imperfect seal, which is bad in its own way). Also, if there's significant background noise, perhaps it is possible to check whether there are any of those background noises coming from the other side of the door. If there are, there must be air to transmit them.
Window observation: check on the other side with a strong light. Sharp shadows from a point source are indications of possible vacuum (warning: the Sun or an illuminated room are definitely not a point source). Dust motes are an almost sure indicator of atmosphere, but there are phenomenons (see Hal Clement's Dust Rag) which might mimic that. Moving shreds of papers etc. would also be telltales of there being an atmosphere. Evidence of explosive decompression would likely indicate there is no atmosphere anymore.
Temperature: if the room beyond the door was full of air and this got out, the lowering pressure should have led to quite a detectable drop in temperature. Then, vacuum being a very good insulator, things would have remained cold. This can be seen in the infrared, or maybe by touching the door and walls until they get heated from the pressurised side. Also, heating one side of the door would give different results if the other side is in vacuum or not.
A likely popular rule of thumb would be if you're not certain that there is an atmosphere, treat it as if it was a vacuum.