Converting multipoint layer to point using PostGIS?

SpatialLite has no way of converting multi-geometries to single-parts itself. There are some 'CastTo' functions but they are for special cases (where your multigeometry contains a single geometry - it won't fan-out). I have seen a reference to a function in the SpatialLite GUI but never found it (perhaps you need to compile from the latest source code. I'm just using a pre-compiled binary). So your best bets are:

• In PostGIS you can use ST_Dump. This is a useful function for expanding multi-geometries.
• In QGIS you could use Vector->Geometry Tools->Multipart to singlepart

You can convert multipoint layer to single points with menu Vector -> Geometry tools -> Multipart to Singleparts and import the new layer into PostGIS.