The most common issues I find when doing airworthiness inspections are as follows;
DATA PLATE - It's VERY important that the information on the data plate (builder name, aircraft model, aircraft serial number) match the info as shown on the registration card (FAA Form 8050-3) exactly. If you use your middle initial in your builder name on the registration, it must appear on the data plate. If you use "Vans RV-6" on the registration, it must appear that way on the data plate. You can't leave out the "Vans" in one place if it appears in the other. Serial numbers must be the same. for example, it can't be "1" in one spot and "01" in another.
The builder name can be an issue for some inspectors because the FAA registration office will always reverse the first and last name. If you fill out your application for registration showing "John L Doe" as the builder, it WILL come back from the FAA with the builder shown as "Doe John L". Some inspectors insist that it be shown as "Doe John L" on the data plate as well. Others will allow "John L Doe". Check with your inspector ahead of time to make sure you don't run into a problem with this.
As a general suggestion, keep your model name as short and simple as possible. Remember that you have to show the entire model name on the data plate and the FAA inspector or DAR has to make it fit in a very small line on the airworthiness certificate. My very first inspection as a DAR was on a Pietenpol and the builder chose the model name "Pietenpol Aircamper 1932"! Needless to say, that didn't fit on the data plate OR the airworthiness certificate. Using "Vans RV-*" is workable, but just "RV-*" is better. Remember that simple is better in most cases.
N Numbers - There are LOTS of aircraft flying around with illegal N numbers. The FAA seems lax on this, but some inspectors go by the book (me included). Usually everyone gets the height correct (3 inches in most cases for homebuilts), but most get the spacing and other dimensions incorrect. Don't depend on your local sign shop or Aircraft Spruce to get this right for you. They do not! (The regulation actually says "1/4 of the character width, but that works out to 1/6 the height, as you'll see below.)
Spacing is the biggest issue. Most everyone gets the characters in the registration mark too close together. There must be one sixth of the height between each character, so for a 3 inch number there must be one half inch spacing.
Width of the character is another possible issue. Width must be 2/3 of the height (except for the number 1), so a 3 inch character should be 2 inches wide from edge to edge.
Stroke can sometimes be a problem as well. "Stroke" is the thickness of the lines that make up the characters of the N number. This must be 1/6 of the character height, so for a 3 inch N number the stroke must be 1/2 inch.
The N number can be either horizontal on the side of the fuselage between the trailing edge of the wing and the leading edge of the horizontal tail, or can be horizontal or vertical on the vertical tail surface. It can NOT be hidden under the horizontal stabilizer, and cannot be diagonal on either surface. It also must be contrasting to the background, uniform in height (i.e., not tapered) and cannot be ornamented in any way. Again, talk to your inspector before you spend a lot of money and time trying to design your N number into your paint scheme. It's NOT fun to have to tell a builder that the airworthiness certificate cannot be issued because the fancy paint job he/she paid big money for incorporates an illegal N number.
These are the things that your A&P probably won't catch. Your EAA Technical Counselor should, but often they get tangled up in the mechanical aspects and don't catch these "regulatory" issues.
Cheers!
Joe