http://purl.org/tcl/home/man/tcl8.4/TclCmd/bgerror.htm is the official man page.
[fill in useful tricks and examples for using bgerror]
Does the documentation describe the calling convention? I didn't notice it. My experience is that the error-handler invokes it as something like
bgerror [firstLineOf $::errorInfo]
During development, one might rush a hack like
proc bgerror message {
puts stderr "An event-based script faulted with '$message'."
}into use.
Tcl syntax help Arts and crafts of Tcl-tk programming Category Command