Tactful way to discuss an error in a published paper I am currently working on my masters thesis in mathematical biology. The work I am doing extends previous work by introducing new biological findings that are relatively recent.

Initially the plan was to take the models in an early paper in the field, reproduce the results, and apply my extensions. But, after a fair bit of work I discovered an error in a model which was bad enough that I couldn't continue to use it as a basis for further work.

This paper is significant in the field (lots of citations, good journal, respected author etc, etc). The error I spotted does have a significant effect on some parts of the analysis. But, to be perfectly honest it's not exactly a world shaking discovery - the original purpose of the paper was to convince researchers in this field that certain mechanisms were plausible and shouldn't be over looked and it certainly did that.

Now, because I found this error, the path of my thesis has taken quite a turn. I've had to propose my own model, perform a similar analysis as the paper, and then apply my extension. In other words I've had to redo a non-negligible amount of the authors work in order to do my intended work.

Discussing the error is important for motivating the extra work I've done. How can I do this tactfully? What is fair to say, and what should I avoid saying? What kind of language should I use? Should I avoid mentioning it altogether?
Use neutral and respectful language, but don't beat about the bush. If the model is wrong, say so. And remember to attack the idea, not the person.

Perhaps say something like:

"This work determined that the while the assumption that [quantity] is conserved is correct in the simpler case of model 1, this does not appear to be correct for the more complex case presented in model 2. This was established by [details of work that lead you to this conclusion]. It was instead found that the quantity is determined by [formula]. Model 2 therefore needs to be amended to [something]."

(I'm not sure if I've quite met all the requirements I've listed, but hopefully it'll give you something to go on.)