My usual method is to adjust the feet so the whole thing is tilted slightly backwards, then gravity does the work. Mostly.
I've got DS18B20 temperature sensors in the fridge and freezer compartments (connected to a Pi via some custom hardware), and alarms (it's complicated) programmed should it exceed a given temperature range. It has to go a long time with a door ajar before the temperature exceeds normal oscillation range, thobut. Also, temperature sensors in fridges are very sensitive to objects with high thermal mass nearby, or the absence thereof. In freezers, the accumulation of ice around the sensor fulfils this function.
Mostly the alarm has been useful for spotting the thermostat misbehaving so I can give it a whack, rather than catching inadequately closed doors. What's more useful is RRDTool graphs of the temperature, which take the guesswork out of thermostat adjustment. (A single instantaneous temperature reading doesn't tell you much, as it oscillates with about a 4.5 hour period.
Basically, if you happen to have a Raspberry Pi sitting near your fridge, wired for attention-getting and logging things to a database, it's well worth the effort of stringing a couple of temperature probes inside. If you haven't, I'm less convinced.
For a door closure alarm, I'd apply the KISS principle and aim to detect the door being closed directly. A finely-adjusted reed switch or microswitch, or maybe something clever with a light sensor. With a simple switch all you need to do is switch a blinkenlight or mildly annoying buzzer, so the person closing the door knows it's worked before they walk away from it.