I don't have a horse in this race (UK Londoner), but there seems to be an awful lot of misreporting about what legal cases are being brought forward by Trump. I've been following it in detail, watched the TV, heard the speeches, etc - there's nothing better to do in lockdown than waste my time on this!
Here's my understanding on what Trump is complaining about, but I'm not sure which state is which - they all seem to have different cases:
Trump doesn't want to stop the counting of votes, he wants to stop votes cast after the election is closed, or postal votes which arrive beyond the end of the voting close.
In one state, Trump is asking the US Supreme Court to make a decision between the State's own Supreme Court and the constitution, which are in conflict. Normally, the close of the polling stations is the trigger to start counting whatever has arrived within that deadline, including postal ballots. However, the local Supreme Court (not sure which state), then decided to allow extra time for the arrival of postal votes timestamped on or before the election day - something which is not allowed in most countries, nor in US, but an exception was made because of Coronavirus. Trump is asking a valid question here - there is a huge opportunity for electoral fraud here. For example, if they allowed extended voting for postal votes, why did they not allow the same extra period for voting in person - also because of corona virus. This will be a tough one for the US Supreme court, because it is unconstitutional, but at the same time, coronavirus is also a problem.
A seond legal issue being raised is that in some states, a lot of postal ballots were delivered to households in their millions - unsolicited. The normal procedure is that the person who wants a postal vote asks for it. It seems that these millions of Postal Votes forms were delivered unsolicited in a very selective way, i.e. to voters more likely to vote for one party than another. That also needs to be looked by the courts, because all voters must have an equal opportunity to vote, and it isn't at all clear what the courts will decide.
Additionally, another court case hinges on that the Repulblican Party representatives were not given access to the vote counting process in some districts - and they should have been. This could result in recounts in those districts.
Finally, in some cases, the case is about specific instances of electoral fraud - these need to be examined case by case.
At the same time, where the results are very close, the Republicans are asking for recounts, and probably the Democrats will do the same if the result goes the either way.
I don't understand why the media are not explaining this clearly, the reporting mostly confuses matters. I guess that most of the media are supporting one side or another, so they are not neutral observers, but rooting for a particular side.
In the meantime, I'm watching this with interest and incredulity!!! This could last for a long time.
Good luck to everyone in US.