You can improve SEO through correct spelling.
Yesterday, Google introduced a new spelling algorithm using a “deep neural net to significantly improve our ability to decipher misspellings.” While this update means better interpreting search queries, perhaps it affects indexing too.
Either way, good spelling embodies the concept of the indirect yet important ranking signal. Anything that increases Dwell Time, or how long someone views a page before possibly returning to search results, is a factor here. Visitors may bounce when they notice careless writing.
Matt Cutts said that better spelling correlates with high PageRank. Bing checks for proper grammar, which means like Dwell Time it probably influences Google as well even if they are officially silent. In the past, Google allowed users to filter by reading level, implying that content sophistication should align with the search.
It seems that spelling, like other copywriting factors, is only a minor signal. However, spelling forms part of the User Experience, which is essential for pleasing your audience and boosting your SEO too.