Oh yeah, that's a thing. You'll get used to it. My guess is that it's a combination of reduced muscle strength combined with thinner and smoother skin.
For dryness, learn to love hand cream (and moisturizer in general for your whole body). I like the Nivea stuff in the blue tube.
As for dropping stuff, I've learned to avoid relying on friction to hold things spiderman-style and instead support them from below.