Lines of text squished together after entering 2 forward slashes

Did you type in the entire URL, or is this some sort of variable or hyperlink reference? Looks kind of like a footnote.

Text variables are a single glyph as far as InDesign  is concerend and they get compressed to fit the available space without breaking across lines, but his looks different -- there's plenty of space left.

If the above suggestions don't help (particularly exporet to .idml) can you share a sample page where this happens?

Do you have any grep style set in the paragraph style applied on the text in question. Does the text disappear or its setting gets messed up, what do you see when you see the text in story editor, if the text ain't missing then this has something to do with styles.

Lastly, if none of the pointers above help, does exporting to IDML and then resaving back to INDD help?

-Manan

Are you using a Paragraph Style?
If so - open the Style and see if there's any GREP Styles, or Nested Styles applied.