Grounding for Common Mode
You should run the ground to the destination of the twisted pair. This keeps the common mode voltage of the twisted pair in check.
In the picture above, the output is interpreted by the receiver as the difference between the two signals of the differential pair. But those signals still have an absolute voltage relative to ground. Obviously both the transmitter and receiver can only tolerate so much absolute voltage. So what is the common mode voltage between them? I dunno. So you should run the ground of the transmitter to the receiver along with the twisted pair to at least give some common base reference voltage that the transmitter and receiver can share. This stop the common mode voltage from straying too far.
It also gives a path for the return currents being sent from the transmitter to get back to the transmitter which reduces noise (the current will find its way back and if you make it a long or difficult path the return current will raise hell). If distances are long enough, the ground line will be at different voltages at each end but keeping transmitter and receiver linked still allows a mechanism for charge to balance out between each transmitter GND and receiver GND so it stops them from straying too far.
For very long runs this still might not be enough to keep the common mode voltage within tolerable levels since the equipment on each end is ultimately grounded to the earth and the mere fact that there is a large distance between the two earthing points means there is a large voltage difference between the two. At that point you need galvanically isolated transmitters and receivers that allow no currents to flow between transmitter and receiver and allow the voltage in the balanced line to float relative to the transmitter and receiver. This lets it tolerate much, much higher common mode voltages. Only digital signals are transmitted this far though but all the same rules apply.
Circulating Ground Currents
You should also connect all grounds together, but connect it such that digital currents do not circulate in the same ground paths that the analog ground currents circulate.
In the picture above, you can see that in the top scenario where the analog currents immediately where the analog circuits are do not get disturbed by digital currents. Sure, near the power supply the analog and digital currents mix together but that's not where the analog component pins are connected to. Technically, the analog currents are causing noise by circulating in the area of the digital ground pins, but digital circuits are much more noise immune because of their discrete thresholds and doesn't affect their operation until the noise gets large enough to cross those thresholds.
In the lower scenario, the the digital currents are flowing straight through the same area that the analog ground currents circulate. This causes noise. This is bad in other ways too because digital circuits are high frequency and there is a larger current loop in the lower scenario than the upper scenario and that radiates more noise as well. The top scenario has a much smaller loop for the high frequency digital currents.
Which reminds me, you need decoupling capacitors in your circuit. Capacitors are short circuits for high frequencies so this gives high frequency currents an even smaller loop to circulate in which reduces noise and makes things more stable. Without them, the high frequency currents have to circulate all the way back to the power supply which makes an enormous loop which radiates noise and causes high frequency voltage dips due to the long wire inductances. The large loop means more inductance which means more voltage dips whenever the component tries to draw a burst of current. The larger loop also makes for a more effective EMI radiator (an antenna).
Place them close to the component pins since you can see from the picture below that having too much parasitic inductance between the capacitor and component pins does not allow a low inductance path for high frequency currents to circulate between the capacitor and component.
A rule of thumb is to use a 0.1uF ceramic capacitor between the power and ground pin of every IC as close to it as possible.
Basically, current need a return path. If you make the path long or difficult bad things happen. That's what all of this boils down to.
All the above examples used a daisy-chained ground, but there is also such thing as a star-ground to let you get around such problems. Remember that wire and copper connections are parasitic inductances.