You can always check what updates will be updated exactly using
yum list updates which would return you a list of packages that have available updates.
Next you could list available updates using
yum list --showduplicates <package>, i.e.,
yum list --showduplicates httpd which would return you a list of available versions for that particular package.
And lastly just update packages one by one using
yum update <package-version>, i.e.,
yum update httpd-2.2.15-39 (or just omit the version and update the package to the latest available version like
yum update httpd
As for what might go wrong.. Well there is a few things worth taking into consideration. Most notable is probably configuration files might change and so you would need to adjust your config files accordingly so just to be on the safe side, I'd backup config files if you haven't automated your server configuration. Other than that, since
yum uses transactions no real threat to your data should occur but if possible I'd still suggest to put your server into maintenance mode (stop websites or software from writing into database or changing files). Other than that most of the time simply running
yum update won't do major version updates and therefore you should have no problems with that.