By Paul Rincon
BBC News science reporter, at the Kennedy Space Center
Discovery's astronauts have been using a 15m-long robotic arm with sensor and camera attachments to examine the shuttle's heat-resistant tiles.
The robotic arm moves across Discovery's surfaces
Video footage of Tuesday's spectacular launch from Kennedy Space Center revealed debris objects falling around the orbiter during its ascent.
US space agency (Nasa) managers had noted an apparent 4cm-wide mark on the nose section of the shuttle.
Nasa officials said it could be a chipped heatshield tile.
The crew's efforts have yet to find any evidence of obvious damage.
And speaking to reporters on Wednesday, the US space agency was keen that everyone should stay calm.
Shuttle flight director Paul Hill said that, based on preliminary checks, engineers did not think the "chipped" tile was going to be a significant issue.
"We can't engineer anything to perfection, so I expected that we would shed some small tolerable amount of debris," he added.
He said experts had yet to decide whether or not to seek more data on the area where there appeared to have been damage in onboard video.
During the second half of flight-day four, astronauts could use the 15m-long Orbiter Boom and Sensor System (OBSS) to conduct further inspections.
SHUTTLE RETURN TO FLIGHT
Mission known as STS-114
Discovery's 31st flight
17th orbiter flight to ISS
Payload: Raffaello Multi-Purpose Logistics Module
Lift-off: 1039 EDT, 26 July
Location: Kennedy Space Center, Launch Pad 39B
Discovery crew: Collins, Kelly, Noguchi, Robinson, Thomas, Lawrence and Camarda
The boom's laser scanner can detect fine damage; the OBSS camera will pick up more obvious damage.
Cameras on the International Space Station (ISS) will also get a good look at the underside of the shuttle when it performs its back-flip manoeuvre as it approaches the platform for docking.
"We've landed with a whole heck of a lot of damage in the 21 years we've been flying shuttles and we have a pretty good feel for different bits of damage on different parts of the orbiter that we know from flight experience that will bring us all the way to the ground," said Paul Hill.
Up and down
Nasa has so far confirmed they are looking at two cases of debris. There are video frames apparently showing a piece of heatshield tile breaking off from the underside of the shuttle.
It was this that left the 4cm-wide white spot near the nose landing-gear doors.
There is also video footage of a dark object falling from the external tank - although this did not appear to hit the shuttle, experts said.
Mr Hill added: "There are some folks in imaging who have found some things they are concerned about on the tank, but I have not been involved in any of the analysis."
The astronauts' arm inspection started at 1045 BST (0545 EDT), taking several hours to complete - and it will be Thursday before it gets a good look at the nose section.
Controlled by computer from inside the crew's cockpit area, the arm can be made to move up and down the shuttle's surfaces.
Additional information on the structural integrity of the spacecraft can also be gleaned from 176 damage-detecting sensors installed in the wings.
Shuttle managers should be able to make a decision on whether there is any critical damage to the shuttle by Sunday.
"We're seeking to understand any instance of tile loss no matter how small," said John Shannon, STS-114 mission operations representative.
"The engineers hope the examination today, and another tomorrow, may resolve these concerns."
Discovery is taking parts and supplies to the ISS.
It is the first orbiter mission by the US space agency since the loss of the Columbia shuttle and its crew in February 2003.
Columbia disintegrated on its re-entry to the Earth's atmosphere because debris-fall on launch had punched a hole in its left wing, allowing super-heated gases to enter the airframe and pull it apart.
Discovery is due to touch down at Kennedy Space Center on 7 August at 0546 EDT (0946 GMT; 1046 BST).