Yes Mike, "multiple critical paths" are objectionable if we are talking about multiple driving paths to the same completion milestone.  In practice, however, the tool being described (multple float path analysis) has several very distinct and valuable uses:

1. To define the driving path to a specific activity in the schedule.  If the contract includes several Liquidated Damages milestones, such as for sectional completions, then each completion milestone will have a distinct driving (aka "critical") path, and the term "multiple critical paths" would be appropriate.

2. To define near-driving paths to the project completion milestone(s) (i.e. near/sub-critical paths).  This is useful for periodic schedule risk assessment and for what-if analyses.  I guess this would also be the main reason for the name, "Multiple Float Paths."

3. Combining 1 and 2 to define the driving and near-driving paths for activities that do not represent project completion.  Emily's link provides this kind of example; "critical path" really shouldn't be used.

As a minor quibble to Emily, I would always recommend using the "free float" option rather than the "total float" option shown in your example.  The latter is affected by activity calendars and by constraints on unrelated activities; it often creates more questions than it answers.  For example, if we ignore the second, parallel report writing activity at the end, your project clearly has a single continuous critical/Longest path extending from the Notice to Proceed to the Project Completion Date.  Running MFP to the Project Completion Date activity using "free float" option will correctly identify this single path.  Re-running the analysis using the "total float" option will identify a new, false path branching from your constrained activity.  That's not correct.