No long-term effects that I know of, aside from the simple on-going fact that I have migraines; they didn't get any worse or more frequent after that, nor have I since developed any other visual or neurological symptoms. As it happens, I don't get migraines very often- once or twice a year. My wife & mother both get them on a much more regular basis, once or twice a
month.
The loss of foveal vision or random patches of the visual field (as opposed to gradual-leading-to-total elimination of the entire visual field) is something I have encountered a few times. As quantumet noted, auras are kind of a grab-bag, different people can have wildly different kinds of visual distortions, and some migraine sufferers don't have them at all. I know one who gets aural (hearing) distortions instead; meanwhile, I don't get any hearing issues, and my wife becomes hypersensitive to sound but doesn't experience distortion.
Migraines, generally, like seizures, are a result of mis-fires in your brain (super simplified explanation, of course). Essentially, something goes wrong such that your brain just decides that it is in pain for no particular reason (although there are triggers, just like there are triggers to epilepsy, that set of just the wrong cascade of neurons). Auras are just another manifestation of the same thing- if the thing that goes wrong goes wrong in or near your visual cortex, you get visual distortions in addition to the pain. Eventually, your brain resets, and then things are normal again, until your brain (metaphorically speaking) tries to read out-of-bounds memory, or goes into an infinite loop, or whatever else it is (again as quantumet noted, the exact mechanism is not really all that well understood), the next time.
Side note, on how everybody's auras are a little different- we just found out about a month ago that my most common aura is blue sparkles, while my wife's is gold sparkles. We knew that we both commonly saw sparkles, just never happened to mention the color before. Also incidentally, I do get auras much more often than I progress to a full-blown migraine headache.
Since the problem is neurological, eye doctors generally won't be able to figure it out or do anything about it. Generally, because eye problems can be migraine triggers. My wife starts getting headaches if she leaves her glasses off too long, and one of the first things to check when migraine frequency increases is whether her prescription has gone out of date. Other triggers are dehydration (for her) hunger (for both of us; this is a problem for me because I don't get hungry normally, so sometimes the first indication that I need to eat today is the onset of a headache) and sleep deprivation (for both of us).