One of the issues I have with most of the time travel/alternate dimension stories I have read on this site is the presence of and repetition of several bits of flat out wrong science that is easily proven wrong.
Please, when writing these stories, do some research into basic facts. I don't usually have an issue with small inconsistencies or wrong facts that don't really affect the overall story. I do have an issue when a wrong fact is presented as gospel truth, is repeated ad-nauseam, and has a significant impact on why something is done or not done in the story.
An example: Several of the most recent time travel stories I have read have all had the MC repeatedly bemoan the "fact" that a stone can only be carved or shaped by a harder stone... and used this "fact" for a basis of not introducing some technological improvements. The MCs were supposed to be pretty intelligent individuals with a broad range of knowledge. So tell me how in the hell did they miss out on the basic fact that you can carve and shape a harder substance using a softer substance if you are willing to devote a lot more time and effort and a lot more of the softer substance in order to do the job?? Basic science here... water wears away stone over time, sandpaper wears away wood/stone, a softer stone can carve a harder stone - it just takes a lot longer and multiple softer stones to do the job.
I can put up with ignoring small inconsistencies or wrong facts...but not when you present them as truths over and over again and use them as a pivot point in your story. Then it just becomes annoying as hell.
Oh... and another thing that is annoying as hell... pay attention to your story's timeline!!
If your MC arrives in the past on say a Monday, meets and has sex with multiple women on Tuesday... they are NOT going to know whether or not they are pregnant by him by Friday!! You can't even tell that fast in modern times with any sort of accuracy much less back in the stone age!! jeesh...