Is it necessary to have a specific intention before each act, or is a general prior intention to obey God's commands in all matters sufficient, such that an act is only unacceptable if the intention was bad?

The intention (niyyah) must be present for every act, to distinguish acts of worship from habits, and obligatory acts from supererogatory ones. The time for the intention is at the beginning of the act of worship. The absence or forgetfulness of the intention during the act does not harm it, provided it was present at the beginning. However, rejecting it during the act invalidates it.