Is it ok to download the latest java update? I thought I had heard of a problem with them?
The Java 6U35 (1.6.0_35) that you currently is rather old, so you should either update to the latest Java 6U41 or Java 7U15 version to be protected against security vulnerabilities.
You can find the latest Java version on the Oracle website.
See Java Platform > Java SE 7U15 and Java 6U41 (Download JRE)