I assume that you mean "since installing Mountain Lion"? You shouldn't be having any problems with Safari or Time Machine. You may need to install the newest version of Safari and you may need to go through Time Machine setup again (there's nothing like having at least one TM backup - I keep two in addition to clones).
For trouble with Time Machine, see http://pondini.org/OSX/Home.html.
For the Safai problem, I would try downloading and installing the latest release of Safari - have you installed the 10.8.2 supplemental update - http://support.apple.com/kb/DL1600?
Clinton, thanks for your help. I am running Safari 6.0.2. No new updates are available for my O.S.: V10.8.2. The problem(s) occur only with Safari, not with Fire Fox or Chrome. One of the artifacts of the problem is a scrambled page with partial type characters and empty frames, a precursor to the freeze. Sometimes, a blank screen. Most of the time, the only way to to emerge from the impasse is to hold down the power key… Force Quit not being accessible.
The problem with Time Machine is that after a few back ups, a dialogue box appears indicating that TM was unsuccessful in creating a new back up folder. By turning off automatic back up, I can manually back up whenever I want. Not Ideal, but workable for me.
For what it's worth, when I run TechTools repair on the disks, The auto back up works… for a while.
I see that others are having similar experiences, so I am not feeling too bad. The applications I use, mostly Adobe CS6, Aperture, and related aps, function well. They also function better with 10.8.2.
I will look into the supplimental Safari update you mention to see if I my version lacks it..
Clinton, I installed the supplimentql Safari update 3 days ago (1/20) and have not experienced any of the aforementioned problems. Safari opens quickly with no artifacts or freezing. Even Time Machine chuggs along in the background.
If this continues, I would have to say you solved my problem.
I had no idea this update was available as the Apple update process indicated nothing additional was available.