What are the practical difficulties that arrise in comparison to using "classic" solder?
Lead free solder typically melts at higher temperatures than tin-lead. This means the solder process puts more stress on the parts being soldered. It probably also relates to it being harder to get a consistent fillet and good wetting when hand-soldering.
Lead free solder is prone to "tin whiskers" which can cause short circuits some time after a board is built.
What causes these difficulties?
Mianly the higher liquidus temperature and lower ductility of the common lead-free solder alloys.
How can they be handled or worked around?
Among other things,
Careful attention to part selection: Make sure all the parts in your design are suitable for use with lead-free assembly temperatures.
Attention to design rules: Provide necessary pad dimensions to provide adequate solder volume and toe-room for fillets. Provide additional clearance to avoid tin-whisker shorts. For really high volume products, arrange parts to allow consistent heating across the board (avoid finicky assembly areas near high-thermal-mass parts, for example)
Assembly process control: Use an assembly shop that will tune the heating profile to ensure good quality soldering. And will inspect outgoing product to catch solder defects and feed back for process improvement.