Hour markers look a bit misaligned.

 

I assume @DLT222 would pick up on that. It's usually the angle of the picture. Very well could be here too.

 

Pretty sure the rehaut is off, not the hour markers.

 

The very earliest Carreras had non-T on the dials, and were also characterized by long and thin hour markers much like on yours. It’s probably worth checking the serial number of the case to see if it makes sense for a non-T dial. Here’s my early 3647T for reference.

Edit to add: I forgot to mention there are several other clues as to whether it’s an early version, such as how the movement bridge is signed and what type of caseback is used. There’s a good reference guide written on Hodinkee (from the early days)…

https://www.hodinkee.com/articles/understanding-the-earliest-heuer-carreras

 

It's fine. As above, the early 3647's had long hour markers, large plain crowns and no T's on the dial.

Later 3647's had the ref stamped between the lugs but some of these early ones did not. Does yours?

Serial around 6xxx?

 

I think you missed an x.... they start around 54000 and go up from there.

 

Is the crown signed? Some people with these early Carreras think they have a replacement generic crown, but the early ones were plain with no logo.
Serial sounds correct for no T.
Looks like a nice example.

 

It seems like a nice example, but that's pretty much a top price for that reference. I know it isn't perfect, but the price guide at the following link can generally be trusted. Maybe that's where the seller looked up his price...

http://www.heuerpriceguide.com/#/carrera-60s/4561057250

 

Looks stunning, price is a bit steep but a very nice one (like this) sold a couple of months ago for 6k€, so it's in line with the market...
Looks all correct, you can compare to my 57xxx 3647 in this article (yes, let me brag a little that they took pics of my watches):
https://www.hodinkee.com/articles/two-early-heuer-carrera-references-3647-7753