Irregular Precision-Recall Curve
This is definitely possible. When you are reducing the threshold, you will never decrease the recall (you can only flag more of the positive examples as positive). Precision is looking at all the examples that you flag positively, and of those the fraction that are truly positive. This means when you are reducing the threshold, you might not add any true positives but only false positives, thereby lowering your precision. Let's take a look at a fabricated example, where P is positive and N is negative. The samples are ranked by score/probability. Everything before the threshold is flagged as positive:

PPNPNNPNNN


If we put the threshold between items 2 and 3, we get a precision of $1$ and a recall of $0.5$:

PP - NPNNPNNN


When we put it between items 3 and 4, we keep the same recall but our precision drops to $0.6667$:

PPN - PNNPNNN