When the TRS-80 goes to read the cassette (usually as the result of a CLOAD or SYSTEM command) the emulator will send the data to the TRS-80 and go into turbo mode to load the data as quickly as possible. Cassette → Auto Turbo can be used to disable this feature.
When the TRS-80 saves a cassette file (e.g., a CSAVE"A" command is entered) the emulator switches to turbo mode. It will prompt you for a PC file in which to save the .cas image when the save is done. If you'd rather just hear the cassette send to the speaker turn off Cassette → Save → Auto.
When auto save is on the emulator waits a fifth of a second after the cassette has stopped before prompting to save the output. In some cases, like when BASIC saves variables to tape, the auto save triggers too quickly. Use the -csd N command line option to increase this delay (given in tenths of a second) or choose one of the presets under the Cassette → Save menu.
When loading a cassette file the emulator displays the cassette counter in the title bar as Cr|123|. When writing the title bar will show Cw|001|. If the counter stops when reading then the emulator has reached the end of the inserted cassette tape image. If the TRS-80 hasn't finished loading then the load has likely failed.