If I reflow a LFCSP IC such as an ADV7180 I probably won't be able to see any solder bridges or unsoldered pads because the pads are under the chip. Can I safely test for bridges by using a multimeter to test for continuity between adjacent traces?
You will need an x-ray imaging device if you did not include test pads on the board for exactly that purpose beforehand.
On some parts a continuity test can give you clues if you have a board that you know works, you can write down the continuity numbers between different pins (or take sample of two or three working boards). Do continuity tests only when the board is off.
Once you have the continuity numbers this can help you to locate problems with a bad part if for example its supposed to be a high impedance input and its near zero. Another gotcha is IC's behave funny when there not powered so don't try and use spec from the datasheet to determine continuity, if you know what kind if input (ESD protected, open collector, open drain, ect then it can help you to determine continuity) it is this can help.
A lot of parts have ESD protection diodes and these turn on in a continuity test so it depends on the part. A continuity test is not a test that will always find problems but it can help during debugging. I've used it several times to find bad parts and then replace them. It really depends on the part but if you have a working board then you can make comparisons.
Another method is to use an IR camera to look for hot spots on the board, this method won't work for shorts between low current signal traces. This method will also help find parts that are dissipating too much power.
A third method is check the power rails and make sure they are in spec.