May I publish the slides from my presentation that use figures from published papers as examples? I used some screenshots from academic published papers (e.g. figures) in my presentation that I gave to a group of colleagues. The screenshots were used as examples of how you should or should not do certain analyses or present certain results.

As my examples concerned screenshots of figures or tables from published paper these fall under copyright.  The copyright is usually held by the editors/publishing companies. The papers/sources are correctly referenced on the respective slide of my presentation that contain the screenshots. 

Still my question is whether it is legal to publish (e.g. make online available) the slides on which the screenshots are given or would this infringe copyright? In other words: do I have to delete the respective slides before spreading my talk?
Yes, it is legal to reproduce and legal to use exact figure if it is not copyrighted.

If you refer to the source, you can reproduce the data. Which means you cannot use the figure by taking a screenshot, but rather reproduce the result by yourself. Data and equations are not copyrighted. 

If the article is in open science or creative commons license (most of them are nowadays) you can take screenshots and use them. 

To avoid complications, why not make your own figure of the data? It is pretty simple. After taking a screenshot, using plot digitizer you can get the data. Use your own plotting tool to make the picture.  This is a problem if your picture is an image from the experiment. Then you need to obtain permission to use that image.