Select and Copy in Safari on iOS Doesn't Always Work Well

I believe this is a design problem with the Select and Paste functionality in iOS when trying to copy content from a web page. If anyone else has this problem and knows a workaround please let me know. Often when you go to select text from a web page, and put your finger down to select text on a web page, you get the blue selection box with anchors, but the anchors are impossible to drag to highlight the specific text you want. Instead, the whole table cell of the web page remains highlighted, and you cannot adjust it to just copy a piece of text within the cell. The selection anchors don't respond when you try to drag them and the while cell stays blue including text you may not want.

This happens all the time to me when attempting to select and copy text on most web pages, both on my iOS iPhone 4S and on my iPad 2, both running iOS 6.1.3 (and on earlier editions of the OS).