Remedial exercise I will leave to Jrahien, he is far better than me in this area.
Form wise I learned to correct mine from a coach at a running club so wouldn't know sites. Ironically I know I likely need to correct my form due to additional weight and physical bulk I have gained in the last couple of years so am trying to figure out anything I may be doing wrong.
When I was doing this for weight training it was easy, video myself with phone, post on here, let the general abuse of correct ensue, say thank you and correct the errors. Running not so easy, by definition I don't stay in shot.
Basics to look at
Soles of shoes, wear should be mainly outer rear heals, but not at the back of the shoe, this shows you landing on the rear outer quarter of the foot, so mostly heel but not full heel strike. Next will be the big toe area from takes offs. Your ideal strike is landing rear outer quarter, going along the outside half of the foot until reaching the ball then going along this and taking off with the big toe. If you have this, brilliant, then there's the deflater I was told after finding mine was perfect, so do over 75% of the population.
Knee to foot alignment. The foot strikes on the outside and takes of on the big toe from the inside so by definition it is not pointing straight forward as you run, unless you are getting it wrong. The angle is slight and changes during the stride, but if your knee isn't matching this it will encounter issues. If you had a view of your foot from your hip it should be totally hidden whenever the knee is bent.
High knees, don't do it. Whenever I hear some witless wonder shouting, 'get those knees up' I want to put their head back into their rectum. You are not running upward you are running forward, you lift your feet off the ground as little as you can to minimise impact. Road runners doing cross country have to adapt in a hurry to avoid tripping over the tiniest pebbles, and this is a good sign. I went from off road to on, and had to shift to virtually no lift to minimise impact. the trade of was a more efficient, comfortable and dramatically faster pace.
Hip position. there are a number of people I see with charming lordosis curves in the lower back, shoving the belly and butt out as they run. The look is known commonly as duck arse, because you look like a Donald while running. The torso should be upright during the entire run, there will be twist in the abdominal region, but this shouldn't affect the linear appearance from the side.
Arm swing. You are going forward, not sideways or diagonally so your arms should go in simple straight lines forward and back, if sprinting this will be a tense line relatively high up, the higher the distance the lower and more relaxed this tends to be. When you see the Kenyans run marathons they look as if you could cut the stings and they would collapse, but they are covering distance faster than most people at sprint. If your arms cross your body you are sending twist through your knees, the risk of this is obvious and you are also wasting energy and effort. This was my flaw and taking time out to fix it was the best thing I ever did for running. I ran my fastest ever half marathon 10 months after starting to amend it and despite being 1.5 times my running weight I have never injured my knees and my average pace has dropped from 10mph when 9 stones to 7.75 now at 13.5 stones, so much as Mo Farah isn't going to be getting nervous I am still considered fairly quick.
Shoulder, relax man, it's just a run. I don't know what it is with people wearing their shoulders for earrings when running. Even sprinters don't do this and they are running as tense as you ever should. As your arms swing your shoulders should be relaxed enough to allow them and get the benefit of this drive. If you don't keep your shoulders relaxed, you will hurt your neck, upper back and breathing capacity.
Breathing. There are very few advantages to being a bipedal mammal, hence we are the only one, but the main one is our ability to run without having to time our breaths. Breathing needs to be relaxed and as deep or shallow as comfortable. The deeper you can go the more oxygen you get but keep this comfortable, increase depth slowly over time if you want to. Don't over think breathing, in through nose, out through mouth because there are nasal hairs filtering crud out, so what, when you are giving it beans your jaw will be slack and you will pull air from everywhere while still keeping it relaxed. You have been breathing for years and if you had been getting it wrong you wouldn't be here.
Clothing.
Shoes need to be right, get gait analysis or what ever to be sure, everything else combined will not be as important.
Support. If you need it wear it. Women using their forearms as a support bra as they run look ridiculous and are messing up their technique so much they are injury time bombs waiting to go off. If you have areas that are in need of support do it. As a male mine is dealt with by the inner part of running shorts, but I have know guys running with boxers and loose shorts complaining about bruised testes. It isn't rocket science, if something swings around, contain it.
