It dont effect unless you change the keyword effectiveness too. use more keyword as permanent template link..
The changing on Blog theme won't give any effect on SEO IF you can remain old on-page factors like the previous theme you used. Here is some on-page factors you would consider to keep them remain the same 100% or as much as possible - H Tags (H1 - H6) - Title Tag - Meta Description / Meta Keywords - Bold / Underline texts - Homepage content
minor change will not make any difference. but if you do a complete face lift and totally change things around, then it will impact on your ranking
yeah sometime some sites are not able to make out the changes done and shows in their original form only and when it redirects to the original form a error mesage dispalys unable to found.It happens with some of them.On a whole it doesnt affects a lot.