They both come up as private.

I'd agree with the core work/tightness on squats. Depth looked fine, but you do start with hip drive and then somehow your upper body takes over to push the weight the rest of the way, because you're leaning too far forward. Maybe deload a bit and let your core catch up? I was leaning forward way too much also, and that's why I started to include front squats in my routine, to force myself to squat more upright with a straight back, because I always felt like I was going to fall backwards, so I overcompensated by leaning too far forward. Try looking up a bit more, as that might help correct it. It's what I ended up having to do. Neutral/forward gaze doesn't necessarily work for everybody on squats (even though it's what Rippetoe says to do). It certainly didn't work for me.

If hip drive is an issue, try "pushing the floor apart" with your feet on the bottom of the squat. That really helps engage those hip muscles and should provide you with the power to drive the weight up all the way.

Rows -- posture overall was good, back was mostly straight and parallel to the floor, but I noticed your upper back/shoulders dipping somewhat, which may have to do with how you have the plates set up, and it's really nothing major. Maybe try one more plate under it so you lean forward less and it's easier to keep things parallel. I understand how awkward those are, and I know my form gets a bit sloppy too because I'm not up to the big plates. It sort of looked like you were squeezing your shoulder blades correctly to finish the move, but I couldn't really tell b/c of the angle.

Maybe just overall focus on tightening up for your lifts, especially engaging your core and keeping everything tight and stable, focus on hip drive and being more upright with your squats, and you should be golden.

I agree that core strength may be the issue, but I'm curious about what you do with your breath when you squat. Molly Galbraith of Girls Gone Strong published something (can't remember what/where) talking about how you can use your inhaled breath to help stabilize your core on squats - I basically visualize a balloon that fills my lower torso as I breathe in, then hold that balloon rigid as I go down and up, only releasing the air pressure at the top of the squat.

And the rows look good - watch your head position, and bump your bar up another set of plates so that you don't have to round quite so much at the beginning of the movement. Also, I can't tell if you are bumping your chest or not? That extra little bit of oomph makes them fun, IMO. But I'm weird like that!

I will always say do some core work. I kind of take the mentality that the core is the foundation to all strength so a focus should be made to get and keep it strong.

Here is a pdf on some really good core stability stretches and exercises. http://www.princeton.edu/uhs/pdfs/Lumbar.pdf

I usually do core on my non-SL days just for the time factor.

Some of my favorite moves are:

Bicycle crunches
Russian Twists
Leg lifts
V-ups (I can't go the full V yet, but it is still a good movement)
Supermans
Wood Chops (I use a kettle bell, resistance band, or cable pull)
Back extensions