How is a MSc thesis evaluated in an application to a PhD program? I am planning to apply to a PhD program in applied mathematics next year, and by that time my MSc thesis (which is in pure mathematics) should be finished.

In case my research results are not significant enough to be published in a journal, how will my thesis be evaluated for the sake of the admission process? Will someone from the committee actually read parts of it (note that a potential advisor will probably not be very familiar with my MSc field)? Will my research potential be judged solely based on my references' recommendation letters referring to my thesis/research? (In which case, is it even worth putting effort in how the thesis is written, assuming my grad school is happy enough with it to award me a degree?)
Given the fact that is extremely rare to have a decent publication out of a Master thesis in pure maths, the content and quality of your thesis will be reflected on the recommendation letters.

This, together with your grades and other activities you may have would be the ticket to your admission. 

Note that nobody will read your thesis. For the admission committee should be enough if it is apparent from the letters that you did a decent work in your thesis. Your application should show that you have potential of doing research but nobody has the time (or the will) to go through a thesis document.