Hello, probably this is not a joomla issue,
and because this is not an identified issue,

• for asking "help", it is better to post here:

http://forum.joomla.org/

Error "1064" sounds like "Mysql syntax error 1064", and it is of no usefulness without the full error message:
we need the SQL error message (if you do not see it already, then go to Joomla Global configuration and enable "debug system" and "error reporting")

Also

• you need to mention PHP / MySQL version numbers (Got System/System Information)
• it sound likes either the DB tables were not upgraded or you have some 3rd party extension that needs to be updated to work with J3.5.0

e.g. 3rd party extensions that add extra options / fields to the article form
you need to update them if you have not done already

1. Re-extract the J3.5.0 zip package into your joomla root folder (and delete "installation" folder)
2. Go to Backend menu: Extensions/Database/Fix (to make sure that all DB tables were updated)
3. Update your all your extensions

4. if the problem persists , get the SQL error message and post it here but also here:
   http://forum.joomla.org/
   
   as this is not a support forum

• if inside the SQL error you can identify a (table) name that reminds you of a 3rd party extension, report the error to the web-site of the author of the 3rd party extension