Never been a real fan of core-specific work.
Very occasionally I'd do reverse ab-curls.. and sometimes prone bridges...
But I've felt that squats+DL's have worked my core enough. As to telling if your core is holding you back..is it collapsing? Or does it stay nice and braced and strong during the lifts (squats/dl's)? Any lower back pain that isn't doesn't seem to be linked directly to bad form?
I dunno, if you aint doing specific core work, do some and see if it helps?
As far as working on other weak points...
I'd say, that given your lifts, that you don't have any weak points just weakness overall.
Just doin the main lifts at this stage will get you stronger.
But down the track..
say you are consistently miss BP after the halfway point, towards lock-out. Maybe you need to work on your tri's, do some iso-tri work or close grip BP or board presses.
Or that you consistently miss DL's at knee height, maybe it's time to do some rack-pulls.
Or squats in the hole, maybe it's time for bands, or box squats..
Do you see where I'm trying to say? Weak area's generally tend to make themselves pretty obvious. But at your stage in training I'd say just keep on with those main lifts, and you'll get stronger. You just don't need the complication of "advanced" training at this stage.
As far as my experience goes- I was missing alot of oh presses at the lock-out (past my forehead). So I did some tri-isolation work and it helped me bust through a plateau.
Was lacking explosiveness out of the hole in squats, so did box squats for a while, also helped me get the numbers moving again. Doing box squats was actually mainly to help with my regular squat form, which prob. helped my numbers too..
The only other issue that I should bring up is the issue of injuries and them being related to weaknesses..
I personally have very weak ext. rotators and poor scap./general shoulder stability. So I have to do a fair bit of work to keep my shoulders in good shape. But again, these things tend to make themselves pretty obvious.. Like, my shoulder clicks, hurts, slides out of joint kind of obvious.
As long as you are doing a balanced program, and as long as your lifts for opposing muscle groups stay fairly balanced, I don't think you really have anything to worry about.
Although I do try and encourage people to add some shoulder-health stuff to their program, regardless of how healthy they think their shoulders are. It just seems that it's the most common complaint from lifters. Esp. people who insist of having BB BP as their main upper body push movement.
Hope this was helpful!