The reviews of The Core tended to talk about Bruce Greenwood's role rather than about his performance, so we've collected as many mentions as we could find. Please be forewarned that there is some spoiler information within a few of these items:

But mainly "The Core" works because the characters are idiosyncratic enough to seem authentic but not so zany that they seem contrived. Hilary Swank is Rebecca, a chipper but driven co-pilot, serving under a commander, played by Bruce Greenwood with his usual humane gravity.
Mick LaSalle, SF Chronicle 3/28/03

Bruce Greenwood, the soft-spoken Canadian star of films by Atom Egoyan, is the ship's captain, .....This interesting gang plays it pretty straight
Steven Rea, Philadelphia Inquirer 3/28/03

The Core, which comes down to a bunch of gifted actors (Hilary Swank, Bruce Greenwood, Delroy Lindo) trying to out-earnest each other as they sit around a cockpit and cruise through digital magma.....
Owen Gleiberman, Entertainment Weekly 4/4/03

The actors come off surprisingly well. They turn in performances that are a step above what you typically receive in these kinds of movies ...... Eckhart, Swank, Greenwood, Tucci and Lindo are all very capable actors, and they do what they can with the material. Most of them play it straight.
Ain't it Cool News 9/17/02

A List actors dine on B-move cheese: A mismatched crew is assembled: plucky young astronaut(Oscar-winner Hilary Swank, in a role Elizabeth Berkley would kill for), her square-jawed CO (B.C.'s own Bruce Greenwood, who was probably hoping to get in some skiing during off-days in last winter's shoot), brilliant, scruffy prof (Aaron Eckhart), wingy inventor (Delroy Lindo) and the foppish scientist........After a promising beginning -- the action sequence where Swank and Greenwood have to land the shuttle and the played-for-laughs preamble to the mission -- the movie bogs down...
Glen Schaefer Vancouver Province 3/28/03

The ship is placed in the capable hands of Col. Robert Iverson (Bruce Greenwood), and Maj. Rebecca Childs (Hillary Swank) as they team with Zimsky, Brazelton, Keyes and Leveque to save the planet.
Gareth Von Kallenback MovieEye 3/03

And who better to drive this craft than the pilots who gave the shuttle such a hair-raising ride, Commander Robert Iverson (Bruce Greenwood (news)) and Major Rebecca "Beck" Childs (Hilary Swank (news)).
Todd McCarthy Variety 3/24/03

When the original commander (Bruce Greenwood) is killed, his second-in-command, and the only woman on board, Maj. Becky Childs (Hilary Swank), reluctantly takes charge.
Louis B. Hobson Calgary Sun 3/28/03

Major Rebecca Childs (Hilary Swank) and Colonel Robert Iverson (Bruce Greenwood) are space shuttle veterans in charge of piloting and navigation, respectively.
James Berardinelli Colossus 3/03

There's also rising NASA star pilot "Beck" Childs (Hilary Swank, aerodynamically sleek) and her somewhat inferior superior, Col. Iverson (Bruce Greenwood).
David Elliott, MSNBC 3/03

And yet the scene is a hum-dinger. The Earth's disturbed magnetic field has confused the shuttle's guidance system, causing it to aim for downtown Los Angeles. Pilot Bruce Greenwood insists "it's Mission Control's call," but co-pilot Hillary Swank has an idea, which she explains (ital) after (unital) the shuttle passes over Dodger Stadium at an altitude of about 800 feet.
Rober Ebert Chicago Sun Times

And an off-course space shuttle is saved by an emergency landing in the L.A. storm drain canals by a plucky pilot, Major Rebecca "Beck" Keyes (Hilary Swank), and her staunch flight commander, Robert Iverson (Bruce Greenwood).
Michael Wilmington, Chicago Tribune

We have the Brilliant Young Scientist Josh Keys (Aaron Eckhart); the Pompous, Famous Scientist Conrad Zimsky (Stanley Tucci); the Eccentric Recluse Scientist Edward Brazleton (Delroy Lindo); the Wry European Scientist Serge Leveque (Tcheky Karyo); the Cocky Computer Hacker Rat (DJ Qualls), the Square-jawed Military Leader Col. Iverson (Bruce Greenwood) and the Hot-shot Young Pilot Becky Childs (Hilary Swank). Overseeing them are the motherly NASA official called "Stick" (Alfre Woodard) and the hard-core military man Gen. Purcell (Richard Jenkins).
Margaret McGurk Cincinnatti Inquirer

Early in the story, a shuttle piloted by Hilary Swank and Bruce Greenwood crash-lands in the Los Angeles River.....In the Utah desert, the U.S. government secretly assembles a team of "terranauts" -- Swank and Greenwood -- and brainy scientists
Kirk Honeycutt Hollywood Reporter

In addition to the trio of scientists, the terranauts include: Commander Robert Iverson (Bruce Greenwood) and his No. 2, Maj. Rebecca "Beck" Childs (Hillary Swank).
Kenneth Turan Los Angeles Times

The commander of the crash-landed space shuttle (Bruce Greenwood) takes charge of the mission with the tomboyish Major Rebecca "Beck" Childs (Oscar winner Hilary Swank) as second in command, and a French atomic weapons expert (Tcheky Karyo) along for the very dangerous ride with Josh, Zimsky and Braz. You can count on brave deaths occurring in roughly reverse order of the actors' billing.
Lou Lumenick NY Post

A startling, unwelcome touch of reality is provided by a core-related emergency landing of a space shuttle, saved with a nifty bit of fast-thinking navigation by young astronaut Rebecca Childs (Hillary Swank) and her less nimble commander, Robert Iverson (Bruce Greenwood), both of whom join the mission.
Hap Erstein, Access Atlanta 3/28/03

THE CORE (Jon Amiel) is far more entertaining than it has a right to be. Indie star Aaron Eckhart plays a college prof who figures out that the earth's core has stalled, which sets the inevitable ragtag band of over-achievers (Hilary Swank, Stanley Tucci, Delroy Lindo) on a mission to the centre of the earth. The premise is full-on big, dumb disaster movie, and the science is no doubt fiction, but The Core knows how to have fun. It's a thrill to watch such a strong indie cast sink their teeth into popcorn entertainment. It's Indiegeddon! Rating: NNN
Cameron Bailey, Now Magazine 3/28/03