Is it worth my time to pursue legal action against my landlord?

You weigh the seriousness of the injury and decide.

She cannot kick you out by reporting a hazard on the property. You injury is to small to do anything legally.

You'll have to decide that for yourself. First, you should consider that you have to prove the landlord was negligent in order to have a claim. You have to show that step was a hidden hazard that the landlord knew or should or should have known about and failed to fix it, or guard or warn you against it.

What is a "tweak" worth in court? $100? Will cost you that just to file.

You should get your knee examined right away to determine what injury you sustained before you decide how you want to proceed. Next, you should take many photographs of the broken step and hang on to them in case the injury is significant enough to warrant the bringing forth of a claim. Also, you should report the incident to the landlord so that there is a record of the incident causing the injury in event that you do pursue a claim. In the event that you do decide to make a claim, then you should interview attorneys to represent you because you will likely get a far better result with the assistance if counsel than you would without an attorney.

I don't think it would be a good idea unless you're looking at substantial injuries to your kneed, otherwise if your landlord ejects you, it may cost you more to move than you'd get from your landlord for your injuries.