Sorry, what problems are these? The article mentions that institutional investors were unhappy about not getting their usual 15% guaranteed bounce, but it seems to have worked pretty well for Google and general investors.
I don't think you read closely enough. On the low-end, banks were thinking $108 for the base price per share. As it was, the IPO ended up at $85/share because of it being a dutch-auction where most investors played it safe and did low bids. As soon as the IPO executed (at $85) it popped anyway to $100. So Google potentially lost out on $23/share (minus 7-8% cut from banks).
Except it doesn't do that. In an open auction if someone bids higher you know you won't get any shares unless you raise your bid.
In a Dutch auction if you keep your bid low there's always a chance you will get your shares and at a good price. As actually happened in the Google case. Yes you're risking you might not get any shares, but bidding higher risks unnecessarily pushing the price higher for yourself and everyone else.
Dutch / English auctions are respectively descending- and ascending-price auctions.
In an English auction the auctioneer starts at a lowball (possibly zero) price and gets increasingly higher bids until he's satisfied that the price can't go any higher. In a Dutch auction the auctioneer starts from a highball price and lowers it himself gradually until he gets a buyer.
A second, orthogonal issue is if an auction is if it's first price (as most auctions: best bidder pays best bid), second price (best bidder pays second best bid) or something more complicated. Economists love the idea of second price ("Vickrey") auctions, but I personally haven't seen it used.
I recommend Bob Milgrom's article "A primer on auctions". It's in the Journal of Economic Perspectives sometime in 88 or 89 I think.
Actually, there's very much a lot to recommend in the Journal of Economic Perspectives whenever you want to learn about something in economics. This journal focuses on publishing accessible surveys of research areas that are just beginning to solidify (and already have a "shape" to them), rather than publish new ideas. It has excellent curatorship and articles tend to be written by top experts in each field.
Note that the term "Dutch auction" is overloaded, but in this case the article specifies:
> Often called a "Dutch" auction, this type of sale allows any investor—institution or individual—to put in a bid over the Web for a certain number of shares at a certain price without knowing what others are offering to pay. After the bidding, the highest price at which every available share can be sold becomes the price for all the shares—the IPO price. Google, along with early backers, was selling almost 20 million shares, and bids could be submitted for as few as five.
This doesn't actually remove the incentive to underbid. You might be thinking of a Vickrey auction? That's an auction of one item, in which the high bidder pays the second-highest bid. (This is what I always think of when I hear "dutch auction".) There's an obvious generalization to auctioning multiple items; but the Google auction is not that generalization, and also that generalization apparently doesn't work.