First let me start by saying that I have heard almost every reason for why B&C is bad and should be non-canon.
Most of them show personal bias or lack of understanding about navy ship procurement and service life.
"Why would it be a down grade for Adam to be posted for the Valkyrie to the Galactica?"
Well assuming the Valkyrie is from the first war lets look at the two ships.
Galactica
Good
1. A first cylon war ship.
2. Highly decorated vassal.
Bad
1. In the reserve fleet (non active duty)
2. About to be retired and turned into a museum.
3. Carry little or no ordinance do to retirement.
4. Had not been updated since the Cylon war outside of new vipers.
5. relic of a past the Colonies were trying to forget.
Valkyrie
Good
1. A first cylon war ship.
2. Highly decorated vassal.
3. Updated with the latest equipment.
4. Still an active duty Battlestar.
5. Part of the class that makes-up most of the Battlestar fleet.
Bad
1. Smaller then Galactic.
So he was on a active duty ship, that was the mainstay of the fleet. And from what you can put together from the series where the largest ships outside of the Mercury class on active duty.
Then he was transferred to a ship in the reserve fleet that was about to be retired and turned into a museum.
Anyone in the military would look at this as a demotion, or a more respectful discharge from service in his case.
"Why did the Valkyrie bridge look so advanced?"
This one is simple, upgrades. This is a standard practice in most navies.
Look at the USS Midway lunched in 1945 and retired in 1992
And yes these are both the same ship.
" The Valkyrie looks like a post war design."
Maybe to you, but to me it looks like a less advanced design then the Galactica/Columbia/Jupiter-class. (Not sure on the class name as I have heard nothing saying that BSGD is canon)
Reasons for my belief.
1. Valkyries exposed jump core shows an older design that had not yet overcome the obstacle of an embedded jump core.
2. Very boxy design that show me underdeveloped hull armor technology compared to the more angler design of Galactica and Pegasus.
3. As has been stated Valkyrie type ships Show up in
Caprica
P.S. The Valkyrie seems to fill the role of a Battlecruiser in the Colonial Fleet, not a destroyer.
"Why does the Galactica's CIC and launch bays seemed to be much more highly advanced and automated early in the war?"
1. So here I assume they were retrograded do to the cylon network infiltration tech later in the war.
2. We don't see the Galactica again until it is about to be retired and turned into a museum so we have no bases to just how it should look when it was fully active.
Overall I see no issues with B&C.