F4, F#4, and G4 are notes that can give you troubles until you have worked at stretching chest voice enough beyond those notes that they then seem relatively low and easy. They are important notes. Ken says these are actually the most beautiful of the tenor notes. You have to get good and comfortable with them, though, or they won't sound as beautiful as they should.
You are falling just a little bit flat on several notes in this clip. I think you probably should go through Ken's Basic Pitch program if you haven't already worked your way through it. It can strengthen you in ways you may not realize with regards to pitch. You can find the Basic Pitch program here:
The Password is PitchFix101
You have a nice-sounding voice and you are keeping it bright. Actually a little more low end would be a good addition to your tone, along with the bright sound you are using.
I think you are singing from your throat and need to move to increased support and sing more from your core.
My advice is to keep doing the exercises diligently to strengthen your voice, increase your range (especially in chest voice), increase support, and also work through the Basic Pitch program.
Please don't be discouraged by me being direct with you on opportunities for getting your voice dialed-in. I want to encourage you to work on these specific things to get to the heart of the matter of turning your weaknesses into your strengths. That's exactly what each of us needs to do: Pinpoint areas of opportunity, and make them shine!
Good Singing to You!