Starting from the basics: Mayonnaise, as you know, is a combination of water-based liquids, water-soluble ingredients, and lipids (fats/oils). Since water and lipids are immiscible, that makes mayonnaise an emulsion.
Because the droplets (of fat) suspended in an emulsion are not actually dissolved, the properties of that emulsion depend entirely on the size of those droplets and their dispersion. The most likely reason that your mayonnaise tasted like oil is that it actually was pure oil in spots.
The technical term for this is flocculation.
(source: Cube Cola)
This is probably what happened to you - it's possible that if you had really poor dispersion, you might have even been closer to the "coalescence" stage.
To use a more tangible example, consider what happens when you dissolve flour or corn starch in cold water, then heat it. The starch gelatinizes and you end up with a fairly uniform, thick paste. Now think of what happens if you toss it into hot water; you'll tend to end up with something that isn't uniform, instead you'll end up with big globs of cooked flour floating around in thin, cloudy water.
Keep in mind that the chemistry is completely different with an emulsion - in fact, there technically is no chemistry happening with an emulsion until emulsifiers come into the picture - but the concept is the same. You might not be able to see those globs of oil floating around in the water as well as you can see the globs of flour, but if you didn't get proper dispersion and suspension, they're there, and they will taste exactly how you'd expect a glob of pure oil to taste.
Traditional mayonnaise uses raw egg yolk (containing lecithin) and mustard (containing mucilage), both of which act as emulsifiers. These are called "emulsifiers" mainly because they help the emulsion to stay stable, which is why the store-bought mayonnaise doesn't separate (it also probably has a few extra additives). However, they aren't all that helpful for getting that initial dispersion; the most efficient way to do that is to let small drops of oil into a liquid that is being constantly and uniformly agitated.
You can do this by stirring, but an even better way is to use an immersion blender with emulsifying blade. Note that this is not the flat aerating blade that is often confused with the emulsifying blade, nor is it the star-shaped liquefying blade that is the default on most sticks and many manufacturers confusingly call an "emulsifying" blade. The one you want looks a bit like a hubcap; it's flat with several slits or holes and is sometimes also called a "smoothie blade" or "whisk blade":
or
(the one I'm talking about is the bottom left)
These things are perfect for preparations like mayonnaise, but if you don't have one, you can get halfway decent results with a wire whisk. You'll just need to use a lot of elbow grease.
If you get really good dispersion, and use sufficient emulsifiers such that the emulsion doesn't separate too fast, then I promise you, your mayo won't have that "fatty" taste and it will be 1000 times better than the store-bought goop.
I've got one of the professional series Kitchen Aids (and my parents have the traditional version to compare and contrast). If money isn't a huge deal, then getting the professional series comes with a more powerful motor and a heavier base that will stop the mixer from "walking" around the counter if you put dough or something dense in the mixer.
One odd thing that I didn't expect is that the mixer is really inconvenient for small things. It can whip up like a triple batch of whipped potatoes, but it has the darnest time whipping up a little bit of whip cream or a little merangue.
Kitchen Aide's attachments are pretty rock solid... One of our more "fun" attachments that we have is the ice cream bowl. Freeze the bowl, dump the ingredients and set the paddle on low. Again, with the professional model, the motor is strong enough to churn a bit longer than traditional other ice cream churns...
IMO, if you're a big dough cook, go w/ the stronger model, otherwise the smaller models should be great.
EDIT
In an interesting note, my sister has one of the smaller models and it did infact "walk" off the counter a few weeks ago... The whole machine went crashing to the ground... She picked it up, dusted it off, but the only damage was a small piece of plastic broke off... Gotta give it to Kitchen Aide
Best Answer
I'm taking a stab here, but since you're accustomed to making mayonnaise in a food processor, you probably already have a habit for how you pour in the oil. Since a food processor moves so fast, it can emulsify quickly, so you can pour the oil in relatively quickly.
A mixer is much slower, like using a whisk, you need to pour the oil very slowly, so every drop becomes completely emulsified before more is added. So try it slower next time.
For this mayonnaise, try to fix it as if it's broken, as in this video
Put another egg yolk in a mixing bowl and slowly add your thin mayo while whisking (or mixing in your mixer). Then slowly add more oil until the consistency is right.
BTW: See how slowly she's pouring?