I get alerts whenever a plane squawks 7700, using a popular flight tracker application. It happens quite frequently that the aircraft, reported to squawk 7700, in actuality squawks 7550 or some other benign number.
What would cause this? Are the instruments such that it starts on 0000, and allows setting each digit with a dial you can turn both left and right?
A transponder in most planes look something like this
(source)
The code is changed by turning the knobs beneath the numbers. Lets say you are assigned 5700 as your code but your previous code was 7456. If you are careless or start from the right most knob your transponder will briefly be set in 7700 until the most significant digit is changed. If the radar does a pass (interrogation) at that time ATC will momentarily receive a 7700. Some people say you should put your transponder in standby (SBY) mode when changing codes to avoid this happening.
Some GA planes (and even some larger planes) have newer digital interface transponders like this one,
(source)
These make it a bit harder to pass through the codes since you are not turning knobs but in bumpy air you could accidentally double tap a number. For example lets say you are assigned 7003 in bumpy air. You go to hit the 7 and accidentally double tap the button. Then you type in the 00 and your code is complete by the time you hit the 3.
After some looking it seems that larger aircraft user a transponder like this one,
(source)
In this case you will see a similar case to the first transponder listed. If its not in STBY while switching you inevitable have to pass over 7700, 7600 or 7500 to get to some codes. If an interrogation happens at that time it may cause the results you mention.
In terms of switching to STBY mode, the only documentation I can find about keeping the transponder in altitude reporting mode is this document which states
operators and pilots of the need to ensure that transponders are in the altitude reporting mode whenever their aircraft is on an airport movement area at all airports.
This was issued in May of 2015 and seems to be related to the ground surveillance systems being installed at airports.
The FAA FAR touches on transponder operation in S91.215 and part C reads
(c) Transponder-on operation. While in the airspace as specified in paragraph (b) of this section or in all controlled airspace, each person operating an aircraft equipped with an operable ATC transponder maintained in accordance with Sec. 91.413 of this part shall operate the transponder, including Mode C equipment if installed, and shall reply on the appropriate code or as assigned by ATC.
This section simply states that you must "operate" the transponder on the code assigned while in required airspace. That seems a little vague and does not completely exclude putting it in STBY mode to switch codes.
For example lets say you are assigned 7003 in bumpy air. You go to hit the 7 and accidentally double tap the button. Then you type in the 00 and your code is complete by the time you hit the 3. <-- This is what that nice friendly "CLR" (CLeaR) button is for. Most pushbutton transponders have one :)
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Some people say you should put your transponder in standby (SBY) mode when changing codes to avoid this happening. - Note that ATC discourages this, and expects the transponder to stay on ALT and the pilot to change codes with care to avoid emergency squawks.
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In the older GA transponders where the code selection was made by turning knobs, the electrical contacts are made thru wafer discs in the back of each individual knob, with time and constant use is possible that the digit indicating disc slips and you'll end up squawking a different code than the displayed on the unit.
Probably the most common scenario would be switching from VFR to a code in the 75xx, 76xx or 77xx ranges when using a transponder with a control to set each individual digit (or each digit in order):
(source: aircraft-spruce.com)
If you're squawking VFR (as most will be) on approach to a towered airfield and are assigned a squawk code 7625, if you're not paying attention you'll set the 7, then the 6, and at that point you'll be set to squawk 7600 (comms failure). Some IFF systems can interrogate an aircraft several times a second, so if you're set to 7600 even for a second it can cause an alert on the ATC system.
To guard against this, The easiest way is to set the transponder to "SBY" to prevent it responding. As other answers/comments have said, this is questionable because it stops altitude reporting, which can be useful even if your squawk code is wrong while you're changing it. Another possibility with the older four-knob analog-display systems is to set your transponder's last digit first when changing from any XX00 code, and in normal left-to-right order when moving into an XX00 code. Say you're squawking VFR and ATC asks you to squawk 7625. Set the 5 first in the last digit, then the 2, then the 6 and finally the 7. You'll transition from 1200 to 1205 to 1225 to 1625 and finally 7625, all completely innocuous codes (though one might be a dupe of another assigned code; really no way to prevent this except to go to standby or just set the code quickly).
It's also possible for newer digital systems to temporarily enter a standby-like mode while you're changing the code, making it harder to accidentally respond with the wrong code, including an emergency code, while you're still switching it. If you exit the code entry mode halfway through, it can still be an issue, and some of the digital systems mimic the four-knob style and so they don't really know when you're done.
