What should I know about "press fit" connectors?
For starters, that connector has an insertion force of 0.75 Newtons per pin.  There's 110 pins.  Converting to lbs and multiplying by the number of pins gives us almost 17 pounds of force to insert.  

Q1:  17 Pounds of force doesn't sound like a lot, but when you're pushing that into a PCB you can easily bend/warp the PCB to the point that components that are already soldered will get messed up-- especially BGA's.  You will need some sort of bench press to push the connector in, and some sort of jig to hold the PCB so it doesn't bend too much.

Q2:  Make sure that the plating of the hole is the correct thickness.  Also, make sure the PCB thickness itself is going to be good with that connector.

Q3:  Check with the manufacturer on the solder-ability of the connector.  It might have platings on it that are more suitable for pressing than soldering.  Also, the plastic used might not stand up to soldering temperatures.  Even if you can solder it, you might want to make "some" of the pins press-fit if only to hold the connector in place while you solder it.  If only 4-12 holes are press-fit then flexing and insertion force will be much more manageable.

In all cases, there is probably information on the manufacturers web site that addresses these issues with more accuracy than what anyone here could give you.  Check for application notes and white papers.  If you are doing volume production then call your mfg rep or distributor for help.