As mentioned above depicting future tech is always going to have a dating problem unless you can think way out of the box, and even then it's iffy because you're still influenced by what you're familiar with.
I still like the briefing room console and it would have been nice to have seen that style reused or adapted more. I like a lot of the shuttlecraft's main control console. Conceptually there is still a good amount of very advanced tech in TOS even if it could be displayed better. If I were to really go whole hog on enhancing TOS some of the control panels could be cleaned up.
Two props I still really like are the lighting panel Reger uncovers in "Return Of The Archons" and Flint's viewing panel in "Requiem For Methuselah"---both are very sleek and simple. Today a lot of flat panel TV's have no visible controls (they're usually discreetly along the side or back) primarily because everyone uses the remote.
I think we can assume that while it isn't really shown or directly referenced there is a lot of stuff being done automatically by a variety of computer systems (in universe). There would have to be for a starship to be truly functional. Kirk mentions (in "Wolf In The Fold") that the computer runs the ship, but I think there has to be be more than one at work. It's possible the reference could be taken as referring to the main computer which exhibits a limited form of artificial intelligence as opposed to a more advanced form as seen with HAL in 2001.
For the general public computers were still essentially magic technology and while a lot of ideas were no doubt floating around in research labs and universities there mightn't have been much understanding as to just how far computer science could go.
Then again in some episodes we did see advanced computer systems. The war computers in "A Taste Of Armageddon" shouldn't be much different than gaming computers we have today. The androids seen on TOS particularly in "What Are Little Girls Made Of?" and "Requiem For Methuselah" show a good measure of sophistication. The Landru computer and Val are two other advanced computer systems.
As referenced upthread the M5 and Gary Seven's computer are more like what we should have seen aboard the Enterprise, not only in how they looked but in how they appeared to function.
It has been said that we are likely to see evermore computer integration into our everyday lives and possibly to the point where we'll take it so much for granted we won't consciously recognize it anymore. Indeed a lot of stuff we use everyday has computer tech in it even if we don't recognize it as such. Our cars (and ships and aircraft) have onboard computers. Tablets and smart phones are small handheld computers as are gaming consoles. We have desktops and laptops and our televisions are becoming more computerized as are our home appliances. We're going to see computers integrated in ways a lot of us can't even imagine yet.
This line of thinking has been explored in SF literature, but (as usual) film and television is generally lagging in that respect.