I am opening my dining room and I don't want to compromise the structural integrity. The previous entryway was supported by two 2"x8". The new entryway is supported by two 2"x4". The new support is spread across nearly the entire wall. The columns are supported by 3" wedge anchors. Is this ready for drywall? How likely is it that an inspector will approve it? The current opening is 5'4". Thank you.
It depends what is above the doorway. A big header like that is somewhat unusual. Is there a beam or something heavy, like a bathtub, above the doorway on the next level?
In general, you can't eyeball something like this. You have to do a bunch of calculations to figure it out. If the new header is not rigid enough, what will happen is that it will bow over time and the ceiling plaster could crack.
Inspectors are not expert structural engineers, and even if they were, as I said, you can't just eyeball it. Without making specific calculations there is no way to tell how stable a structural member is. Usually plans get approved ahead of time, that is when the structural approval is given. The on-site inspection is just to verify that what is built is the same thing as what is on the plans.
So, to answer your question: it will get approved if it matches the renovation plan and the renovation plan was approved.
Usually when framing is altered a structural engineer signs off on the plans and the city simply assumes it is sound if a registered engineer signs it.
How likely? In my area about a 1% chance. It completely obvious that the previous setup was done as a load bearing wall. You have done nothing to prove that it isn't load bearing. You don't even mention in your question which way the joists are running above and below this floor. So my answer to your question is absolutely no.
And below is my opinion of how I would react walking into your home:
I see a posted wall. I see a double header. I probably saw the 2x8 laying on its side when I initially checked it. I would instantly think that you are the biggest hack I can imagine. On a scale of 1 to 100 this is 95ish on the hack job. Mainly just because how easy it it would be to do it right.
Who the hell flips a 2x4?
Why would someone go through all this work and not get rid of the post on the left? I am certain that this beam could be gone with a header that is not wider than your 2x8. Huh?
I would quadruple check every part of your project down to the smallest thing. As an inspector I wouldn't trust anything you did. You are basically putting a bulls eye on your back. I don't suggest you show this as is.