Is there an idiom for making the same mistake repeatedly?

"Treading" sounds odd because "to tread on" implies intentional stomping which isn't as comic/funny. In English I think we'd just say "They keep stepping on the same rake."

Other idiomatic images might be "They keep shooting themselves in the foot." or "...walking into the same wall."

Or for failed political systems one might say "Building castles out of sand."

More common is to simply say "Some fools never learn."

Also, the quote is actually: "Insanity is doing the same thing over and over and expecting a different result."

It's not uncommon to hear someone disapprovingly say, "this is like groundhog day," if they witness someone else repeat a mistake frequently.

groundhog day: a situation in which a series of unwelcome or tedious events appear to be recurring in exactly the same way.

"Incorrigible", "unreformable", "irrecoverable" ? This all suggests a certain imperviousness to improvement, which might be slightly different, since you're probably asking about an unwillingness rather than an inability to change.

Maybe the simplest option is to simply say they "keep making the same mistake".

I'm aware of several idioms with different flavors, each pertaining to some but not all of the situations you listed:

• bankers (or banks, for that matter) who scheme, swindle and cheat, and get burned, yet resume their murky activities once the dust has settled can be described as dyed-in-the-wool cheats.

• politicians (or political parties, for that matter) making an attempt, again, to make a system of ideas work that has failed many times in the past may be flogging a dead horse, as may people arguing with their spouses of many years even though neither party can recall a single instance of their fighting yielding even remotely satisfactory results in the past, especially if they're fighting about the same issue. Or if it's the action of arguing or running for office and not the issues at hand, the problem could be that you can't teach an old dog new tricks and these people don't know how else to deal with their problems.

• folks purchasing $100 worth of lottery tickets every week for years on end: this may be an example of the sunk cost fallacy, or throwing good money after bad, depending on why they're buying the tickets.

• The slapstick in Tom and Jerry, as far as I can recall, is often predicated on repetition of different kinds. There's rhythmic repetition of the sort depicted in the Garfield comic, where a character suffers the same injury repeatedly but in a very short timespan and while they're still reeling from previous blows; I don't think the character flaws implied by the idioms and words in this and other answers apply, as the character isn't necessarily able to learn from the last mistake in time to avoid the next. However, another kind of repetition draws humor from the idea that the character is a slow learner (or too slow a learner to outwit the adversary/environment), which brings it back to quietsign's answer.

as (something) as they come TFD an idiom

Said of someone or something that displays a trait or characteristic to the utmost degree.

As in:

X is as stupid as they come.

From the book of Proverbs in the Bible:

As a dog returns to his vomit, so a fool repeats his folly

As a wikipedia article explains,

It means that fools are stubbornly inflexible and this is illustrated with the repulsive simile of the dog that eats its vomit again ..

In English, shooting yourself in the foot is a useful idiom to describe a dumb mistake. It is mostly used for single instances, but can be used in the repetitive sense OP wants, as in this National Review headline, "President Trump Keeps Shooting Himself in the Foot."

But for me, the (somewhat vulgar) idiom that immediately comes to mind is stepping on your own dick. Unlike "shoot yourself in the foot", this expression is much more commonly used in the repetitive sense than to describe isolated instances:

"Why can't Trump stop stepping on his own dick?"

"How Do I Stop Stepping on my Own Dick?"

My dude can't stop stepping on his own dick right under the "Remember not to step on your own dick" sign. https://twitter.com/markagee/status/871182213529739264

GOP Benghazi Press Conference Basically Just Trey Gowdy Stepping Repeatedly On Own Dick

IMO this expression comes closest to what OP was looking for: it's about stepping on something (a dick instead of a rake), it's colloquial, it conjures up an instantly memorable (and arguably hilarious) mental image, and it's typically used to describe repeated instances of bumbling stupidity rather than a single one. (It should also be noted that it does not connote that the bumbler is well-endowed, but rather that they are exceptionally clumsy--imagine the contortion a typical person would need to actually step on their own genitals.)

That said, this saying would definitely not be appropriate in some professional contexts, and it's pretty gender-specific, too.

But in almost any context where you would say someone "keeps treading on the same rake" in Russian, you could replace it with "keeps stepping on their own dick" to get across much the same message (and humor) to an English speaker.