I think at your skill level all the advice that should be given is in relation to your macro mechanics., so simply put constatnly make scvs and always try to have your money as low as possible.
You build order seems quite inefficient, with you sitting only on one unit producing structure for quite some time, and it also takes you a while to get up your orbital command, which hampers your economy. Say if you had built your barracks on 12, gas at 13, orbital at 15, then factory and second refinery when you have 100 gas, followed by starport right after you could have had your vikings up much more quickly. You also let yourself get supply blocked. What I do is work my first three supply depots into my build, generally 10, 16 and 22, and then have an scv constantly building supply depots.
Although your mechanics are the most important thing to worry about, you also have to question your long term strategy and what you want to do. Vikings are strong in that situation because they can bypass the rocks and get in some good scouting, as well as snipe the opponents medivacs, but they aren't strong in a direct fight if your opponent went, say, mass marauders. In conjunction with tanks however Vikings are great, as siege mode tanks can shoot farther than they can see, so Vikings can give the tanks that extra bit of sight.
I've included a replay of one of my TvT where I open up barracks into factory into starport to show you a smooth build, and the kind of thing you should be aiming for. My plan was to get a banshee from my starport, and use that in my initial timing push, then switch on a reactor and start building vikings and use them with tanks as described above. It can adapted for your viking build though, by just making a reactor instead of a tech lab, or no add on at all.