Drag shocks

What problems do they cause on the street?

Well,several. A general rougher ride over bumps and such but a loose "floaty" feeling when driving faster than 35 mph. The car may not track well-meaning it might wander on the road if the surface is rough as you won't have smooth,even control over the springs. More oversteer and less cornoring g's. I agree with ironmedic,70/30's are livable but 90/10's should be reserved for track or weekend play toys only.
 
I have 90/10's and 50/50's on my daily driver.

Speaking specifically of shocks, the 50/50's are the same as stock, I believe. The 90/10's do float a little bit but not enough for it to cause problems while driving around in the street. Seriously, you'll only *really* notice it when you lay on it in a straight line or try to push a turn too hard. Drive it normally and it'll feel almost the same as stock.
 
I picked up 70/30's and drag shocks but I was already spending like $550. Then a wave of common sense hit me, I searched for Tokico 5-way adjustables and got them for around $450 shipped to my door tax and shipping included off ebay( I returned the drag suspension). We put them on and it is a night and day difference. Let me put it this way - I haven't even adjusted it to the "drag" or "loose" settings yet because I love how they respond on the tight setting - yeah apparently I had stock struts and shocks in my car - these were a MAJOR upgrade! I took a right hand 90 degree turn going 30 and threw the car sideways and it gripped so hard that I almost overcompensated for the roll like my "old" suspension previously handled - I suggest going adjustable, its cheaper, more versatile and will relatively accomplish the same goals as the ALL drag setup.

If you go ALL drag like you stated, then go ahead and pick up a set of 4 cylinder springs from a mustang junk yard and install them on your car - that will save you a couple hundred bucks and has the exact same effect of drag springs too.

Good Luck