What should/can I do on finding an error in a published article?
Here's what I would suggest:


First, alert the authors to the issues. Wait to see how they respond, or do not respond. But in all cases, they should be the first you write to.
If the issues do not severely impact the correctness of the work or its utility, stop there. It's probably not worth making a fuss about something most readers will either not use, or can easily correct themselves. 
If you publish something on the topic yourself, especially if you build on the authors' equations or otherwise use them, you should make a note of the issue in your article.
Finally, if you believe the issue is important and/or the equations are widely used, you should contact the journal's editor and ask for guidance.


Errata are “authored” by the original authors. Publisher's corrections also exist, when the responsibility for the issue (typo in equation, misprint in figures, etc.) is that of the publisher.