Main difference between Recorder and Player is that Recorder runs under your user account (usually domain account) but Player (by default) runs under local user account. This difference can cause different proxy settings (most common) - Recorder uses proxy but Player not - or different IE settings.
One thing to try is to set Player to use domain accounts for playback. There is a configuration tool "c:\Program Files (x86)\SolarWinds\Orion\SEUM\Player\SolarWinds.SEUM.AgentDomainConfigurationTool.exe" that can be used to setup domain accounts.
There is one known issue related to proxy in domain is it's configure using PAC script. We have seen cases when this configuration script was not applied to Player domain accounts until someone logged under these accounts to player machine.
Do you have some specific kinds of failures that you see on player? Some pattern?