I noticed the pilots would apply more thrust just before coming into land
This is fairly normal. Firstly increased thrust is necessary to overcome the increased drag caused by the gear and flaps. It also has the added benefit of having the engines spooled up ready for a go around. Spool up time on larger turbo fans can be a fairly long time, and if you're near the ground you need power as soon as you can have it.
It really depends on how the approach was flown. If the deceleration and configuration was left fairly late then you could end up going from flight idle to, roughly, 50% power within a few seconds. And as you've pointed out this can makes nervous passengers feel a bit uncomfortable.
pretty hefty landings
I couldn't comment on the 737, I've never flown one but, as F3G says a smooth landing isn't always assured. But please remember that a
good landing is in the right place at the right speed...and you don't break it! Nothing else.