To be fair, the author is a fresh law school graduate. What does he know about whether legal practice is inefficient or not?
I was a summer associate at a large New York law firm, and the level of technology was fairly typical for corporate America. We had a centralized document management system that integrated version control and generation of deltas. We had a centralized, searchable repository of every document generated for every client, which we could use to avoid duplicating effort when doing new work. We did everything via Blackberry e-mail and Outlook calendaring.
Beyond the generic "you can always have better document management" I'm not sure what else there was to do. The major legal research databases (Westlaw and Nexis) have god-awful interfaces, but there isn't much law firms can do about that, since there is a huge barrier to entry in that market (the proprietary databases).
The fundamental problem is that nearly everything you do for a client is a one-off. It's 90% similar to what you've done for a previous client, but that remaining 10% is not very amenable to technological automation. Can you write some software that will cross-reference an SEC disclosure against the client's big pile of haphazardly-assembled internal documentation, which are handed over in God-knows how many formats? If so, then you're going to make some serious money. If not, then well that's how that graveyard of failed legal technology companies builds up.
The big recent advance in legal technology has been software to speed up document review, which leverages document search technology that has really improved (and obsoleted a large number of discovery attorneys in the process). Law firms have been quick to embrace such software, as well as services such as "in-sourced" discovery centers in places like West Virginia. To date, legal technology hasn't advanced much beyond that, largely because computer technology for working with documents hasn't evolved much beyond search.