Five examples I give of why memory tests can leave a lot to be desired. That doesn't mean they're useless, just that unless the psychiatrist or other person administering them is savvy, they can be inaccurate and that it's well worth giving an explanation of your answer or, if you're with someone else, explaining their answer. Bear in mind that whilst they're characterised as 'memory' tests, they also test other things that are relevant.
1. Hearing
I had a memory test some years ago and the psychiatrist was asking me to remember three random words. He had his back to a brightly lit window and he had some sort of African accent with very loose lip movements. I asked him to repeat words, but you're not supposed to say them more than three times. In the end I gave up and said if he couldn't be bothered to write them down or fingerspell them, I wasn't going to play guess the word.
Other issues such as problems with vision, speech etc. can be relevant, as can the use of English as a second language (which may not show from accent or nationality).
2. Familiarity/habit with question
I enjoyed a conversation on Facebook once. I'll paraphrase it.
"I had a memory test today. The doctor asked me to remember where John Smith lives. Apparently, he still lives at 42 High Street, Manchester."
"When did he move there? I'm sure my psychiatrist said he lived at 42 High Street, Cardiff."
"No, he lives at 42 High Street, Aberdeen."
"But I thought he still lived at 42 High Street, Cambridge."
The thread lasted a lot longer than that. Lots of fun speculation about why John Smith keeps moving house.
3. Familiarity/habit with task
Counting backwards in sevens is bog standard. But there are two main problems with this that I can see.
Firstly, if you haven't been asked to do this or haven't done it for years, it's a test of calculation and memory. If you've been having memory tests for years, including before your memory started to go, it's a test of long-term memory. Your line of work or social interests could be relevant to this.
Secondly, some people actually do this to get to sleep. No, really. Then you're checking what I think of as 'habitual memory'. The backwards in sevens test would still be useful, just that the results would need to be interpreted differently.
That being said, slowness could be misinterpreted. I'm obsessed with getting stuff right and checking it, so my instinct would be to work out the nearest multiple to a hundred, work out the difference, and count backwards by the familiar figures, adding on the difference. An example - "Hmm, ten sevens are 70. That leaves 30. Four sevens are 28. So each number I need is a multiple of seven, plus two. Three sevens are 21, which, added to 70, gives me 91, so the next one down is 91 + 2 = 93."
But what's being tested with me isn't what's being tested is if you think this way (which I suspect is more common) "A hundred minus seven. So I need 90 + (10-7) = 93." Etc.
4. Social
I took Dad to a dementia clinic. It was in a health clinic building he knew back to childhood. To soothe him taking him there, I told him he was going for a 'free health test for elders' and that they'd probably check things like his memory.
When we got there, a young woman came out to fetch us and took us into a room and started asking questions. She sounded a bit pushy. She demanded of Dad "Do you know who I am?" After a long pause, he said "I think the correct modern term would be senior executive."
I made an excuse to leave the room with her, telling Dad I needed to sort some administrative stuff. In the next room, I pointed out to her that she hadn't introduced herself. She wasn't wearing a name badge or other clinical role indicator such as white coat or stethoscope. I was guessing she was a doctor or nurse but I didn't actually know.
I pointed out that the room had absolutely nothing in it to indicate that it was a clinical room. However, my father had remembered that he was in a clinical building and his career had involved visiting hospitals in a formal capacity, being the VIP/bigwig.
But she didn't introduce herself or brief him, so she wasn't a director or senior manager. She came across like a jumped-up secretary as she demanded "Do you know who I am?" so whilst his memory mightn't be good, his logical deduction and manners were excellent and he'd given the socially correct response.
5. Not knowing what you're asking
A friend took her friend, whom I'll call Edna, to a memory test. The psychiatrist did the usual pre-test waffle, then got started.
"So, Edna, when were you born?"
"1928."
"And who's the Queen?"
"Mary."
For some reason, the psychiatrist thought Edna had given the wrong answer and that the correct answer should be Elizabeth. My friend and Edna are both historians, still actively interested in history in retirement, and both have a background in teaching, and put him right, parsing the question.
'Who' is a question word, asking for identity or translation. Thus if someone asks "Who is the queen?" and we have a queen, it could be interpreted as asking for the name or other identifier, and whether or not we do, it could be interpreted as equivalent of "What is a queen?" prompting something like "Head of state" or "King's wife."
The question asked was "Who's..." That could be "Who is..." or "Who was...?" If "Who is...?" it could refer to the past, which would be particularly common in certain sorts of documentary and narrative, where the past is spoken of in the present. What my generation called the historic present. (I think they call it something else now.) Usage of present tense to indicate past in everyday speech varies massively according to things like social class, region etc.
Normally, a "Who's...?" question would be interpreted as present tense, i.e. "Who is currently...?" but if there's a time indicator such as "These days, who's the queen..." then that should be taken into account.
And there was a time indicator "And." The question was "And who's the queen?" or, in other words, "Who's the queen in 1928?" The correct answer therefore was Mary of Teck, who was queen and empress consort to George V from 1910 to 1936.
Conclusion
Don't write off memory tests as meaningless, just soothe friends and relatives if they're subjected to them badly, and clarify responses where helpful. E.g. if you're asked something yourself, you might clarify with "Who was the queen in 1928? That would have been Mary."
(Amended for typos not content.)