How does DC offset affect a signal?
DC offset adds noise floor and causes low level distortion. This is typically inaudible, however it may become apparent when the sound is altered in some way, such converting it to an MP3, or altering its frequency, and so on.
Can DC offset damage speakers?
DC signals also affect the movement of the speaker cone which may result in a reduction of audio quality, although this doesn't damage the speaker.
Does DC offset affect slew rate?
As long as the offset is in the linear range, it is not affected by DC offset. Slew rate is limited by two factors whichever is smaller; The main reason for slew rate is current limit. dV/dt=Imax/Cload by either + or - current limiting, if asymmetric .