There's many situations where 1 of the 2 F2L pieces is in the wrong slot. It's often possible to take that piece out in a way that either pairs it up directly, or makes the pieces ready for an R U R' insertion.
Take advantage of empty slots. For example case 15 can be solved with U' R' U R U' R U R' if the back/right slot is empty, or U L' U L U R U R' if the front/left slot is empty. Both are faster than anything you'll find at standard F2L guides.
Keep re-grips to a minimum. If you need to do L' U' L, then the U' can be done with a push of the right index to avoid a re-grip with left hand.
No pair should take more than 11 moves. Look up F2L algs on for example AlgDb if you can't find anything good for cases, but try for the most part to understand how the algs work rather than memorizing the moves.
And more things you can learn eventually:
2 Sided PLL recognition. It is possible to recognize any PLL from any angle, something many of the fastest cubers take advantage of for faster recognition. This post is a good guide with useful links.
X-Cross. This means solving the cross in a way that simultaneously solves an F2L pair. Some examples of easy x-crosses you can start using:
You notice that your cross will also solve a single corner/edge. See if there's an easy way to insert the corresponding corner/edge where it belongs, so the whole pair will be solved once the cross is done. This method works best if the last move of the cross solution is D/D'/D2.
An easy 2x2x2 block can be solved before the two last edges are inserted.
A pair might be already built or nearly built, and it might be easier to solve it during the cross rather than trying to preserve it.
Plan first pair in inspection (Cross+1). This goes side by side with x-cross, and builds on the cross-to-F2L transition. The end-goal is that you will be able to plan either cross+1 or x-cross during inspection every time. X-cross sounds great in theory, and it is often great too, but there's also many cases where it becomes too hard or convoluted to plan, and that where cross+1 comes in.
Lookahead for OLL/PLL. I don't think anyone can predict OLL and PLL every time, but you can still learn to narrow down the possible cases once OLL and PLL is properly ingrained. Knowing things like "this PLL will have lots of blocks", or "headlights on left" before reaching PLL should help improve recognition time, as you can mentally narrow down the possible cases to look out for. For example if OLL 7 or OLL 33 has a lot of blocks, then it usually means you'll get N perm, J perm or skip. If you know COLL well, then you can start learning how your OLLs affect corner permutation, and then predict whether you get EPLL, or adjacent/diagonal corner permutation.
The first thing to learn for OLL prediction is to be aware of edge orientation while solving the last F2L pair. Knowing ahead of time if you'll get a dot case or cross is nice. Beyond that it mostly comes down to lookahead during the last pair and lots of experience.
Valuable tools and sources:
If you still have trouble figuring out your weaknesses after this, then I recommend filming an average of 5 (preferably with the camera between you and the cube, or behind your shoulder) and post it somewhere asking for for critique. The Daily Discussion Thread of /r/Cubers is a great place for this.
AlgDb - Algorithm Database. Great place to find the most popular algorithms for a bunch of different sets. The first algorithm for each case is usually the best, but there's also room for personal preference in many cases.
CubeSkills - Made by Feliks, one of the best cubers in the world. Has PDFs with good algs for OLL and PLL (plus much more), and video guides for many of the things I've mentioned here.
BestSiteEver - Great tool for practicing recognition of OLL and PLL. You can select the specific cases you want to practice, so you don't have to get cases you don't know or ones you've already learned well enough. The ZBLL trainer can also be used for COLL/CMLL/CLL if you need that.
Tao Yu Alg Trainer - An alternative alg trainer with different strengths and weaknesses. Getting properly used to the controls may take hours, and it doesn't do anything for fingertricks (so you'll have to practice that separately), but it's very efficient for learning the recognition and moves (and connecting those two in your mind) when learning bigger alg sets.
C2F2L - A tool for training cross and cross+1. Set the desired cross length and hold your cube with cross color on top when applying the scramble. See how long you can set the cross while still being able to solve it optimally, and solve it blindfolded. Then do the same with cross + predict F2L corner, and lastly when planning cross + the first pair.
alg.cubing - Great tool every cuber should know about. Paste in algs an follow along at any speed if you have a hard time learning algs while reading them. Or use it to reconstruct solves to make it easier to show it off or ask for critique.
How to be sub-x - Great video series by J Perm covering how to get from your current speed to the next milestone.
Are you wondering about how long each part of the solve should take for someone at your speed? Check out this post. The TLDR (assuming you know full OLL and PLL) is: Cross: 12% F2L: 50% OLL: 16.5% PLL: 21.5%