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It is more effective in reducing drag due to flying close to the speed of sound by about a factor of two over aft sweep (meaning that less sweep is required).
It greatly improves the high angle-of-attack (i.e. low-speed) characteristics of an airplane. This is especially true for stall, where the inflow of the vortices causes the inner part of the wing to stall first, preserving the lift over the ailerons and keeping the airplane from going out of control. (Stall characteristics are difficult to predict and are often solved experimentally through flight testing which is horrifically expensive, forward sweep can help with this)
Forward sweep has a negative effect on the lateral (roll) stability of an airplane, which needs to be taken into account.
Forward swept wings that are constructed conventionally have the structural divergence problem you discussed. However, the flight control system is not how the problem is overcome. The structural design of the wing must be stronger against torsion, a twisting motion. This imposes a weight penalty that may or may not be outweighed by the advantages mentioned above depending on the specific aircraft.
Two significant problems arose in the data reduction and analysis process. These included uncertainties in angle of attack upwash calibration and effects of maneuver dynamics on drag levels.
Many of the problems with FSW designs have been overcome with composite fibres and fly-by-wire systems.
Grumman flew a testbed aircraft - the X29 - for quite a while in the pursuit of research and information.
Until recently, FSW has been unfeasible due to several major barriers (like wings ripping off from the stress), so there are no operational military or commercial FSW aircraft that I know of. I seem to remember several companies such as RUTAN and others like that experimenting with FSW personal aircraft, but I don't know if anything has reached fruition.
These days other technologies have basically neutralised any advantages FSW may have had over conventional rear-swept wings, so it's probably unlikely that we'll see FSW aircraft.