Your comments

I have no explanation for the fact that it seemed to be more sluggish at first.

But it's good to hear that it's better now :)
Thanks a lot! Now I see where you're coming from. I'll add switches to the app settings because I think that most people don't want to have their source code auto-corrected.

Writing an ebook in html is a use case where this does make sense though. That also explains your feature request about html entities ( :)
What are you using Textastic for? For HTML or source code I don't want to have a spell checker or auto-capitalization. This only makes sense if you just enter normal text. Maybe I'm missing something?

I might add a switch to settings that would allow you to enable these features.
A movie would certainly help!
Well, this certainly doesn't sound like the sort of delay I see. I was talking about tenths of a second.

What kind of file (file size, file type) are you editing?
I assume you're talking about the auto-indentation? Textastic looks at the current line. If there are tabs in front of the first character, it uses tabs, if there are spaces, it uses spaces.

Or do you mean that hitting the "tab" key should insert spaces instead of a tab character?
Thanks for the screenshot! Yes, the syntax highlighter doesn't like alphanumeric characters in front of quotes.

So, in your case, the syntax highlighter does the right thing when you insert a space after "echo" like this:

echo '<p align="center">'.$copyright.'</b>';

Sorry for the inconvenience.
That's actually possible with 3). You can edit the recently opened files or mark a whole folder to keep a local copy of it.