Inconsistencies with re-branding?

Not NI, during the virtual globe era at any rate. It was "BBC1 Northern Ireland" visually but rare in that era for announcers to say the full name (usually just "BBC1").

ITV's 2006 rebrand started out with the launch of ITV4 in November 2005, where it straight away used the 2006 branding. There was a logo in the 2005 ITV Annual Report that was originally planned to be used for ITV4, but that was never used on screen at all. That was followed by the rebrands to ITV1, ITV2 and ITV3 in January 2006.

CITV continued to use its old branding until the launch of the CITV Channel in March 2006.

ITV seemed to change their minds about whether brands like ITV2 should have their own separate identity back then. When ITV2 launched it had its own unique logo, but when the ITV1 name came into use in 2001 it adopted the same generic style. After a couple of years however it broke off and developed its own reversed colour scheme before getting a completely different look from the 2006 rebrand.

Apparently before the 2006 rebrand, ITV was concerned that ITV2's identity perceived it as an extension of the main ITV channel. It was the case to an extent as ITV2 showed a wide range of programming that wouldn't fit in on the channel today, including archive shows, and sport.

The launches of ITV3 and ITV4 managed to enable this overhaul in presentation - it became a young-skewing channel (even more so since Be launched).

I think ITV2 was always supposed to be a young skewing channel (as the launch trailers featuring then-teen-popstar Billie Piper indicate) but at the start it was more of an ITV Extra. As you say there was sport programming, but there was also things like GMTV2 and CITV2 and shows hosted by people who wouldn't be seen dead on ITV2 nowadays.

ITV's digital strategy (as in digital TV and not whatever it means this week) of the 2000s was very smart, moving sport to ITV4 and creating an equivalent channel for older skewing programming in ITV3 (still my nan's favourite TV channel, fact fans)

A 'prototype' stripey BBC2 was used on some holding slides in the late seventies. Here's an example:
https://youtu.be/pAthfPZCkAs?t=1m9s

And here's the more familiar version of the 2, with the full channel name in stripey-style, in 1980:
https://youtu.be/DVDfSCNThbc?t=1m37s

Discussion of branding on the BBC2 test card reminds me that the slanty-boxed /B/B/C/2/ COLOUR logo remained in use on TCF well into the eighties - until about 84, I think.

I think that's because the test card was a physical slide- and presumably it was easier to leave it as it was rather than change it. Though for BBC1 they just superimposed a grey bar and "BBC1" in the Anchor font over the "BBC2 Colour" legend.

And if my guess of '84 is right, that would coincide with the switch from a slide to an electronically-generated Test Card F. Wandering OT - Seem to remember a newspaper article around 1983, saying Carole Hersee wouldn't be seen on the test card in the future, as the slides used were being damaged by heat. Wonder if the Beeb really considered scrapping TCF, or whether Fleet Street got it wrong?

Probably a mistake by the press - they correctly reported that the test card was getting replaced, but it was just an electronic reproduction of F, and not a new design.

Didn't the BBC flirt with an electronic testcard that wasn't TCF to replace the optical TCF, then implemented an electronic version of TCF in the end?

Yes, Test Card G I think, that was a modified version of the Philips PM5544

http://www.radios-tv.co.uk/Pembers/Test-Cards/Test-Card-Technical.html#PM5544

That had been around and in use by the BBC years before 1984 though, so would they have been considering "replacing" TCF with it?