As you might guess, the type of oil you use affects the taste of the mayonnaise. I suggest that you start with the oil you regularly cook with and then experiment from there.
I've found that the biggest reason for failure is putting in too much acid (lemon juice/vinegar). The result is something akin to soup. Nothing will correct this failure. However, you can use this mayonnaise-soup in potato salad (or other similar salads).
You can add small amounts (up to 1 tsp) of spices, such as mustard (dried or prepared) and Tabasco sauce. Add these to the egg/acid mixture before pouring in the oil, so they get thoroughly mixed into the mayonnaise. This mayonnaise will normally keep for a maximum of three weeks if kept in a cold part of the refrigerator (such as the bottom shelf away from the door)
Aviva Garrett Santa Cruz, California, USA Excelan, Inc., San Jose, California ucbvax!mtxinu!excelan!avivaRecipe last modified: 6 Nov 86
Path: decwrl!recipes From: aviva@excelan (Aviva Garrett) Newsgroups: mod.recipes Subject: RECIPE: Mayonnaise Message-ID: <7880@decwrl.DEC.COM> Date: 30 Jan 87 04:48:27 GMT Sender: recipes@decwrl.DEC.COM Organization: Excelan, Inc., San Jose, California, USA Lines: 64 Approved: reid@decwrl.UUCP Copyright (C) 1987 USENET Community Trust Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the USENET copyright notice and the title of the newsgroup and its date appear, and notice is given that copying is by permission of the USENET Community Trust or the original contributor.