I know it's only been a week since I started my "Train Every Body Part Every Day Program" but I thought I would give you my feedback so far...

One concern I had was potential strain on my joints, especially my elbow/bicep area where I tend to get flare-ups even when doing traditional split workout programs. So far so good, and I think this is because I'm distributing the stress on these areas throughout the week rather than hitting a specific pull day and really socking it to my elbow joint and then paying for it for the next few days. Same would be true for my knees when doing a dedicated leg day.

In terms of strength gains it is way too soon to tell but my repeat Day 1 Monday workout went well and I feel I was a bit stronger compared to last week, this could simply have been a good workout day, we all have good and bad workout days.

I forgot to mention one other benefit to hitting every body part every day. And that is, it really doesn't matter how many days you workout each week  since you will always be hitting each muscle group evenly. So if you miss a day it's no big deal and if your schedule does not allow you to workout the same amount of days each week then this type of program could work well for you.