"The deliberate use of a weak element that will fail in order to protect other elements in the system from damage." - Universal Principles of Design
Unit tests could be seen as a form of weakest link in that we want the system to fail in our tests instead of in our production environment. Pre-condition and post-condition assertions (remember Bertrand Meyer don't you?) are the perfect example of weakest links in software design. The assertion fails, then the program stops or does something intelligent about the detection: logging the anomaly or dropping an incorrect record. We have more options available to us when our weak link fails in software than other domains. I would even put exception handling under the weak link design umbrella.
So, why don't we use it more? It's rare I see pre-condition assertions at all. I know the performance overlords declared them to be bad. But, when you have Rails running high traffic websites, does a few extra assertions really matter? I think not. I would rather have my program run slower with safety belts than doing something catastrophic with my data. Brian Foote once gave a talk where he equated pre and post conditions to the goalie in a game of hockey. And asked the question, "Would you want to play with or without the goalie?" It's a statement that's lived with me since.
With that being said, are they places in your current design that could use a few more fuses?