What are common problems encountered when using a double pulley system?

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For starters, the lower pulley 'splits' the force the platform is pulling down with. Also, the drum is pulling on both the cable and the platform it's connected to.
 
The values 1.8kN and 1.2kN are spot on. I don't know where you got 0.9kN and 2.1kN, though. The tension 1.2kN from the drum should cause a chain of action-reaction pairs along every segment of rope.