I'll reveal the answer up front: yes, I do still need to pay attention to Google Alerts. But they're not as important to me as they used to be, and Twitter is the reason for that.
At Smart Bear we make a peer code review tool. Part of my job is to keep an eye on what's going on in the peer code review world: what are people saying about peer code review, who's doing code review, who's not, and what's happening with other code review tools.
I've used Google Alerts for several years to help keep up with what's happening. But Google has its limits - at a given point in time there are many web pages that are not in its index. When a new web page is added, it's unknown how long it will be before it gets added to Google's index. Further, there are some types of dynamically generated pages that never get added to Google's index.
Meanwhile, Twitter has a search feature that I really like: you can get an RSS feed for any search on Twitter. So its like creating a Google Alert for the content of Twitter. I've created Twitter searches that correspond to each of my Google Alerts.
From what I can tell, this page went up on IBM's alphaWorks site on April 21: http://www.alphaworks.ibm.com/tech/ccrt/. It describes a peer code review tool that is apparently a research project at IBM. That's something I would be interested in.
If I were depending solely on Google Alerts to tell me about it, I would have fallen behind the times - it did not show up on one of my Google Alerts until May 15. But there have been multiple tweets about it; the first two I saw were on April 22 (here and here). In this case, the wisdom of crowds found me what I wanted long before the fancy search algorithm could.
So yeah, I still look at my Google Alerts - they do still find things of interest for me. But I check my Twitter searches first.