The short and boring answer that you'll get from me is "not significantly that I'm aware of." (Warning: This answer relies a bit more on generalizations than I'm normally comfortable with, as I am very very far from an expert on Hebrew orthography, so if someone is and wants to correct me on any of this then I'm very interested. The thing I'm really interested in here is Hebrew printing.)

I assume you're thinking of something along the lines of how English language printing contributed to the development of English spelling, the great vowel shift, etc. That wasn't really a factor when it came to Hebrew. The spelling of most Hebrew words has, to a large extent, been standardized for a long time. The only really significant changes have been in the last hundred or so years, with the development of modern Hebrew, and those changes are relatively insignificant.*

It's worth mentioning that most Hebrew books first printed were either a) reprints of much older books, whether (to put it in scientific terms lol) VERY VERY old (like the Bible) or VERY old (like the Talmud) or just plain old (like, say, works by Maimonides, which when they were first printed in the 1470s were about 300 years old). They were basically printed as is, and while of course printing introduces many new forms into different books (such as the standardization of the layout of a Talmudic page) and has the potential to introduce errors, the spelling and grammar remained the same, as they had been standardized long before. (In particular, the Masoretic text of the Hebrew Bible, the standardized text right down to the vowelizations and cantillation [which aren't even written down], had already been standardized for at least 600 years.) Jewish tradition placed a great deal of emphasis on the correct spelling of words in the Bible and you will find many medieval Biblical commentaries assigning a great deal of meaning to the spelling of Biblical words.

In these books, therefore, there was no reason to change any spelling and grammar, because they were being reproduced from previous manuscripts and there weren't really any spelling varieties to correct/choose from. (In general, Hebrew spelling and grammar are quite specific- one letter added, subtracted or change can completely change the meaning of a word or make it meaningless altogether.) In fact, when it came to reprinting old books, Jewish printers relied on their expertise in Bible and Talmud in making sure that their manuscripts were as correct and authentic as possible, with non-Jewish printers who printed Hebrew books hiring Hebrew editors to make sure that everything was authentic. While changes were made, such as in terms of trying to find the most authentic version of a text (such as Gershom Soncino traveling to find the "authentic" Tosafot to include in his printing of the Talmud), as a general rule specific text corrections were made to fix it in line with a previous, more correct version of that text, not to change spelling or grammar to something newly seen as more correct.

When it came to new books which were printed- and in the course of time there were many- their Hebrew continued as it had been. Medieval Hebrew (a misleading name, as it includes Hebrew written at least until the 19th century, and to a certain extent it is still used today by some), the Hebrew used at the time of the invention of printing, was mostly but not exclusively used for ritual and scholarly purposes. While medieval Hebrew had undergone some changes in the earlier part of the millennium, through the creation of the field of Hebrew linguistics and the creation of words as a result of Hebrew/Arabic translation, by the time of the printing press it wasn't changing much. Most new Hebrew language books were rabbinic works, which were written in mostly traditional styles in which rabbis wrote as their own (pre-printing press) teachers had; this kind of Hebrew included many loan words from Aramaic. However, there were no real changes in orthography which could be attributed to the printing press.

Of course, the printing press did introduce some innovations besides the ones already mentioned like Talmudic page layout and text standardization, such as the development of Hebrew typefaces, most famously the cursive that is now known as "Rashi script" (as it became known as the script used to print the commentary of Rashi, or Rabbi Shlomo Yitzchaki, alongside the text of the Bible and Talmud) and which was adapted from a Sefardic Hebrew handwriting style. But orthography was not really innovated.

*Quick explanation- Hebrew is an abjad script, which means that its letters are consonants and the vowels are meant to be implied. However, for the last thousand-plus years it's actually what's called a "dirty abjad," which means that there are some vowel indicators: nikkud (vowel points) and soft consonants (letters which are consonants but are also sometimes used to indicate vowels). For the most part, nikkud was and is not used; however, modern Hebrew changed the spellings of many words by adding soft consonants to indicate vowels, when historically those words had been spelled without them.