I'll start by saying that you are off to an ambitious and promising start. Once you master this style of tying you will be able to tie to match any mayfly.
Now for some hopefully constrictive criticism which may have zero impact on the number of fish you catch but is intended to help you become a better tyer. These are in the order that I would tie the fly.
Tail: as noted, it might be a bit long, but I wouldn't worry too much about that. One shank length is standard. I can't tell from the picture how the tail is sitting. It looks nicely splayed, but should stay on the top of the hook.
Wings: It is hard to see the wings, but they look short to me. They should be at least the length of the shank and I like to make them a bit longer. If the do not stick above the hackle they are really not worth putting on because he fish is unlikely to be able to see them buried in the hackle. Wing placement is a more complicated issue and I'll get into that below.
Body: Mayflys don't have much of a body really, so yours is a bit too heavy with minimal taper. Try to keep the tail end just a bit thicker than the hook and build a slight taper to just behind the wing. Leave space behind the wing for your hackle wraps. Do not dub the thorax area, or at least try not dubbing it and see how it works for you. Some people say that dubbing under the hackle makes it easier to get the hackle to lay correctly. I find that it is more difficult.
Hackle: Your hackle quality is clearly an issue. Cutting is a bad idea because it will change the impression the fly makes sitting on the water. The light pattern produced by the hackle tips (or natural legs) dimpling the water surface is the first thing that the fish can see as the fly approaches. Blunter cut tips are more likely to break through the surface tension, so it will be a very different effect. Standard length is 1.5x the gap, a bit longer is okay on a Catskill style (up to 2x the gap). Try to wrap each wrap tightly in front of the previous wrap. 3 turns behind and 2-3 in front should be enough. If the hackle twists as you wrap, try to compensate for this. You can tie good drys with the type of hackle you are using as long as the size is correct. Lastly, your hackle looks a bit too close to the eye and that makes it tough to cleanly finish the fly. This is set by the placement of the wings, so you might try moving them back a bit.
Additional thoughts on wing placement: I get a bit tied up in detail on this, and you may not care to even think about this at this stage in your tying, but I find it helpful to organize the mess in my head and keep the terms straight. No one has ever really codified it, but basically there are 3 “common” types of winged hackled dry flies, and the type is largely determined by wing placement. The first is the most commonly seen in fly shops today. I don't know if there is a formal name for the style, but I think of it as “modern” or possibly “western” style. The wings are placed at about the 25% shank point and it looks like you hit this dead on. The problem with tying this style is that it pushes the hackle towards the eye and makes a bit of a mess when you have lower quality hackle to begin with. I'm not sure why it evolved to be so common, but I'm guessing it has something to do with the availability of genetic saddle hackle. The Catskill style places the wings a bit further back at about the 30% point and leaves a bit of space behind the eye of either bare hook or a thread head. This style evolved pre-genetic hackle, and I think is the best way for a beginner to get his dry fly merit badge without spending a fortune on hackle. Finally, there is the thorax style which places the hackle at about the 50% point. This style when tied correctly does a fantastic job of cocking, riding properly, and imitating the natural, but tying it correctly is really difficult.
That's a really long way of again saying that you should try tying a few with the wings moved back a bit on the hook shank.
Keep at it, you are off to a great start!
Mike.