Do you have the text set to align to a baseline grid?
First check to see if the text frames are overlapping an object with text wrap applied. One easy way to test this is to turn on Ignore Text Wrap in the frame options dialogue. If this makes the problem go away then a text wrap was your culprit You can either accept that the problem is solved or explore further to see what objects have the text wrap and either remove it or ensure it is appropriate for your layout.
I do not think this is the problem. I think your text is set to snap to a baseline grid. As the frame moves about the page the baseline grid is staying fixed to the page. This makes the first line of text always align to the next baseline grid it can find, which makes the first line shift up or down a bit relative to the frame. In some cases there is not enough rom for all the text.
In the attached image, the text in the frame on the left is aligned to the baseline grid. Since the grid does not match the leading the grid defines the leading. This also makes the text start at the next grid line available, instead of at the top of the frame.
Baseline grid can be turned on and off in the Control panel or the paragraph panel. It is a paragraph level text attribute, not an attribute of the text frame.