When I originally scanned an old book, I just used the straight quotation marks and I want to go back and change them to smart quotes. When I use the search and replace function in Sigil though, it always takes me to the formatting page and not the finished text page, where it's much harder to read through the quotes, and it also picks up every quote around the font styles used.

Is there some way that I'm missing to keep the search and replace on the book view page and not keep jumping to the code view page? I don't want to do a copy/paste into a text editor for it since all the formatting, italics, etc. are done. What I'm doing now is searching in book view, and clicking the correct smart quote from the special character window for replace, which is very slow.
IMHO, it's much easier to fix straight quotes with kiwidude's Modify ePub Calibre plug-in. It has a Smarten Punctuation option that will automatically convert straight quotes to curly quotes.
However, since it's using a heuristic algorithm, you'll need to double-check the ePub after the conversion.
Oh wow, that worked great! I've only used the plugin for removing embedded fonts, didn't realize it could do the punctuation so well. I didn't check the entire book yet, but through the first few chapters everything turned out perfect.

I was worried about the single apostrophes being correct, but it picked those up perfectly too even when they were placed at the beginning of a word. Very impressive, thanks for the tip and thank you, kiwidude!
The Spartypants code is the very first thing I would want to integrate if/when Sigil ever gets a plugin interface.
The plug in interface would be very useful. Cleaning things up in Sigil then having to back to calibre where it will gunk things up does not have much appeal.
This is true. But to be fair... the entire purpose of calibre's Modify ePub plugin is to allow you to make many of these "common" modifications to ePubs without all the gunkification that normally comes with doing a calibre ePub to ePub conversion. So using the Modify ePub plugin to "smarten" punctuation does nothing else to the ePub besides that. No gunk.
I am with Diap
Once I have edited with Sigil, I do not want to do a full EPUB->EPUB conversion on my work. I use Modify EPUB to update covers and metadata
For my situation, the Calibre plugin was exactly what I needed. Originally I went with straight quotes because it was my first book I did and used MS Word and that really messed it up. It was just one less headache to deal with.

Now the book is really finished, all formatting and corrections already done in Sigil. Yes, it would have been easier to do had I thought of it before this point (such as with the Atlantis Word Processor), but having to do it now, after all else is done, I'll have to say that the Modify ePub plugin did an amazing job. It changed nothing else in the book except the quotes and ... to ellipses. I had to change a few of those back, but all in all, it really did an amazing job without changing anything else in the book, everything else was untouched.

Of course I'd love a way to have done it in Sigil first, but that wasn't an option.

Edit: Oops, I take part of that back. For words such as Tis, it used the incorrect apostrophe, it used ‘ instead of ’, but that will be an easy search and replace in Sigil to correct.