My 06 Mazda3 headlight low beam points to the ground and there does not seem to have anything to adjust, either the light bulb (held by the clam sprint very tight) or the low beam housing which is an integrated plastic case with the high beam and the corner lights. Any advice? Thanks.

 

Yes! Absolutely!!
The first thing to do/check is remove the offending bulb from the socket and make sure the plastic adapter/spacer is in place. Don;t ask me why they were designed this way. It's a big PITA and probably the worst, most useless piece of hardware ever designed for a headlamp, but it MUST be in place.
Second, make sure the tangs on the back of the bulb line up with their female counterparts in the healamp housing. This is critical also or the bulb will not seat correctly and can cause the issue you are referring to.
Third, if all else fails and everything is in place as it should be, there are three screws on the back of the housing to adjust the headlamps. From the factory, and assuming they have not already been touched there are whilte plastic caps on the heads that must be removed for adjustment.
The most obvoius screw in the middle, between the individual beams, will adjust both high and low beams up or down. The one below that will only adjust the low beam up or down. That's the one you will need to deal with.
For clarity, the third screw is very near the outside edge of the assembly and adjusts the entire assem side to side, but chances are you will not have to touch that one... and its hard to get to anyway.

I suggest doing everything you can BEFORE trying to make any adjustments using these screws, because getting it back to normal can be a challenge.

Are you the original owner of this car? Was it involved in an accident at some point?

 

Thank you for your great advice. Will be a good project tomorrow!