Yes, I have had another user or two have these issues, but I'm not sure what the cause is. I cannot reproduce the dropdown issue on my system to try and sort it out. It may be some sort of focus issue on certain systems with a particular OS X version. When the focus is not on the entry box, the suggestion box is supposed to disappear.
The "Anchor not Found" matter is when Bible Analyzer is trying to scroll to the current, active verse in a Bible window. If it can't find the verse this warning pops up. However, the verse is found in the image you posted. I'll look more into this.
Developer, Bible Analyzer
But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness. (Rom 4:5 AV)