Hi LEM,
The 737 does have differential spoilers, I have just taken this series of photos to demonstrate.
I-2021 I think the limitation is no speedbrake with flaps greater than 5.
S&L - Still learning about the 737 !
The above series of photographs (737-300) show how the flight spoilers move with various combinations of aileron and speed brake. With speedbrake down, the spoiler simply rises on the down-going wing with aileron. With speedbrake applied, not only do the spoilers on the down-going wing rise but also the spoilers on the up-going wing fall. Notice that even with full speedbrake applied the spoilers still rise on the downgoing wing.
This property of the spoilers on both wings to respond to roll inputs is known as differential spoilers. It only occurs when speedbrake is used which is why the roll rate is increased when speedbrake is used. Boeing recommend that speedbrake is not used below 1000 feet for this reason.
NB In the bottom two photographs the speedbrake lever was only at the flight detent position but because the aircraft was on the ground the ground spoilers deployed. This is why if you have any sort of technical problem that might be due to a faulty air-ground sensor eg QRH "Gear Lever Will Not Move Up After Takeoff" you must not use speedbrake in case the ground spoilers deploy in-flight. You can see from the series of photographs just how much extra drag ground spoilers will give over flight spoilers.