My fellow nit-picking grammar jellies: How should this be written?

Well, you definitely don’t want the apostrophe there but otherwise it is o.k. It might be preferable to write out “mid-seventeen hundreds” though.

Or…the middle of the eighteenth century.

mid-eighteenth century

Whether to include the apostrophe is a matter of style. Which style guide are you following? Look up its prescription for numbers and dates.

“The face of America and its impression…” is awkward and invites misreading. The face’s impression? Please think clearly about what you mean to convey with “impression,” which is vague in this context.

NO apostrophe after the number. It should read: mid-1700s.

( ...and use “all right” rather than “alright.”)

When to Form a Plural with an Apostrophe, which quotes the Chicago Manual of Style as follows:

DO NOT use an apostrophe to form the plural of capital letters used as words, abbreviations that contain no interior periods, and numerals used as nouns:
the three Rs.
the 1990s
lengthy URLs
———

As for using the hyphen, another site quotes the Chicago manual here.

mid- forms one word in combination, unless it is joined to a capital letter or a numeral, in which case a hyphen is employed: midsentence, midcentury; but mid-July, mid-1985.
———

…which is basically what @janbb said in the first place. “mid-1700s” seems perfectly fine to me.

“The Great Awakening of the mid-1700’s changed the face of America and its impression of religion forever.”

This reads to me thus: “America’s face, and the face’s impression of religion, changed due to the Great Awakening of the mid-1700s.”

Perhaps you mean something more like this: “The political landscape (or whatever you mean by “face of America”, as this is a meaningless term) and impression of religion in America changed due to the Great Awakening of the mid-1700s.”

@Jeruba Yes, I found that construction awkward and confusing as well.

@Jeruba and @janbb Oh yes, I changed the wording there, too.

Thank you, everyone!