There's a lot of people in this thread (who have been playing much longer than I have, from the look of it) talking about how they might miss stuff in the chat box directed at them, or they miss things in party/Alliance chat because they're too focused on what's going on. That doesn't have to be the case, though, and you don't need chat bubbles or third party tools to fix it! It's right here, in the Character Configuration settings:
You can set up sound alerts for certain chat channels, including party and alliance chat. Very helpful for dungeons, I've found; there's been a few instances where I've been focused on tanking, and wouldn't have noticed a message in party chat if it weren't for the sound alert prompting me to look over and see what was said. You can also get alerts if someone emotes whilst targeting you!
Granted, it doesn't do anything for /say (how could it, really) and I know that I'm only speaking from the experience of a new player, but it doesn't seem that /say is even used much. Most of the time, if I see something in that channel it's either an RMT bot, or just two/three people speaking directly to each other. 99% of public chat that I see going on between folks is through /shout or /yell.