My amp puts out 180 watts @ 4 ohms, and my sub's RMS wattage is 150, but max wattage is 600. Is there any extra measures I have to take when wiring them up due to the difference, or will it be fine?
Just ignore Max ratings altogther, focus on RMS or continuous power ratings. You need enough power to get your sub to full mechanical excursion without clipping, so the enclosure that your sub is in is going to play a part. If you have a sealed box, you're probably looking at wanting to have right around RMS, and you have headroom, so you'll be fine. If you were running that sub in a ported, you might need much less than that to get the sub to its max excursion. If your amp puts out 180W @ 4 ohms, make sure your sub is 4 ohm SVC, 2 ohm DVC wired in parallel, or 8 ohm DVC wired in series.
Parallel and series is for wiring multiple voice coils. If you were wiring either 2 subs, or 1 sub with DVCs, you could just as easily wire them to 2 seperate channels of a 2 channel amp. Nothing to do with parallel or series there. The way you wire the sub has nothing to do with power handling, the voice coils will still dissipate the same amount of heat no matter how it's wired. A DVC sub gives you wiring options, that's correct.