While nothing as large as 1906 has occurred (that was estimated to be 7.5-8 in magnitude, aka enormous) there have been several 6+ earthquakes in the region including the 7.0 quake in 1989.  These as well as other quakes in California in that time have led to damages and subsequent changes in construction and safety requirements.  A 1906-sized earthquake would cause great damage even today but it would look nothing like what you find in Haiti.

Now, there is a lunar tide, and there is a solar tide. Both mean an oval stress/deformation of the Earth's shape relative to perfect rotational symmetry, which is moving because the Earth's angular rate of rotation and the Moon's orbital speed around the Earth resp. the Earth's around the Sun aren't identical.

Twice every month, when the Sun and Earth and Moon are on the same line -- whether there is a solar or a lunar eclipse, or neither (when the Moon is at a higher inclination) --, the lunar and solar tides are on top of each other. However, the solar tide being smaller, it is not much stronger than the normal twice-daily lunar tide.

_{*Lunatic*, n.
One whose delusions are out of fashion.}

For the question "is the variation in gravitational force large enough to cause tectonic plates to slide?" there are actually hints that they could, even when the gravitational force is negigible in comparison to the muscular power play between plates. The best place for this is to look at the San Andreas fault zone, which is the world's best playground for understanding earthquakes and stress build-up.

There were already strong indications that very large quakes can trigger other severe quakes at the other end of a tectonic plate with a variable time delay. In other words, one heavy quake can be "teleconnected" to another. Recently a Nature publication appeared on the effect of the tides:

Though tides raised in the Earth by the sun and moon are not known to trigger earthquakes directly, they can trigger swarms of deep tremors, which could increase the likelihood of quakes on the fault above the tremor zone, the researchers say. At other fault zones, such as at Cascadia, swarms of tremors in the ductile zone deep underground correlate with slip at depth as well as increased stress on the shallower "seismogenic zone," where earthquakes are generated. The situation on the San Andreas Fault is not so clear, however.

"These tremors represent slip along the fault 25 kilometers (15 miles) underground, and this slip should push the fault zone above in a similar pattern," Bürgmann said. "But it seems like it must be very subtle, because we actually don't see a tidal signal in regular earthquakes. Even though the earthquake zone also sees the tidal stress and also feels the added periodic behavior of the tremor below, they don't seem to be very bothered."

Nevertheless, said Nadeau, "It is certainly in the realm of reasonable conjecture that tremors are stressing the fault zone above it. The deep San Andreas Fault is moving faster when tremors are more active, presumably stressing the seismogenic zone, loading the fault a little bit faster. And that may have a relationship to stimulating earthquake activity."

There you go. :)