No comments please on my pathetic orange twist - this is my very first do-it-yourself cocktail.
I think the twist is not that bad for a first try! If I may give a few pointers that may make things easier for the future:
First, as a generality a twist should only include the peel and none of the flesh underneath. The goal is to slice off a piece of peel from the outside of the fruit without actually cutting into the flesh of the fruit itself. Sometimes this may be difficult if it is a particularly thin-skinned citrus, in which case it is probably not well suited to using for twists. As a generality, thicker-skinned, pebbly-textured oranges are better for twists than thinner-skinned, smooth-textured oranges. So the technique is to use a sharp paring knife and try to slice off just a thin piece of peel with the smallest amount of pith as you can manage. As a matter of practicality, sometimes it's easier to slice off a piece with more pith on the back and then just trim off the pith if you're concerned about excess bitterness in the drink. Another, easier, technique is just to swipe off a strip of peel using a sharp vegetable peeler.
Second, I'd say that your twist is overall too narrow. If you're going for the long type of twist, I'd say that you want a strip of peel approximately 1/2 inch wide. The very thin strips of peel you have there, and elsewhere above, look more like 1/8 inch wide and possibly (probably?) made with a channel knife. This is not a width one would tend to use as an "all purpose cocktail twist." Rather, it's the width one normally sees in something called a "horse's neck" type of garnish, which is an extra-long thin spiral of peel that's usually slid down the side of a highball glass. More to the point, it's difficult to actually "twist" a peel so diminutive and get any oil out of it onto the surface of the drink.
Third, long isn't the only peel configuration for twists. A disk-shaped orange or lemon twist is one that's used by many of the best cocktail bars for "up cocktails" (the long type does tend to be more attractive in Old Fashioned-type and other rocks drinks where it can be slid in alongside the ice). Making the disk type is easy: just slice a round piece of peel off the side of the citrus. One advantage to this kind of twist is that it's easy to hold in one hand and bend over the drink, thereby shooting plenty of oil out of the twist and onto the surface of the drink. Here
you can see Pegu Club's Kenta Goto using this type of twist over a Fitty-Fitty Martini.