Can't confirm improved load times for the BD35 but the load times of the new Panasonic BD55 have improved over the previous BD50. It 'might' be reasonable to assume the BD35 has also improved.
Taken from a recent US review of the Panasonic BD55
First and second generation standalone Blu-ray Disc players were notoriously slow at booting up and playing discs. Panasonic made significant improvements in loading speeds in their third generation players. The difference between these new fourth generation players and their immediate predecessors is not as drastic, though Panasonic has managed to shave a bit of time off the disc loading process.
The initial boot-up time of the BD55 is not far off from that of the BD50. It takes roughly 24 seconds to boot up the BD55 from powered off to the Blu-ray splash screen and another 9 seconds to display the first screen of a Blu-ray Disc ("Hitch") previously inserted in the player. This is about 6 or 7 seconds faster than the BD50. When the BD55 is already powered on, the differences are a bit more substantial. Placing a disc in the tray and pressing "play" takes around 20 seconds for a Blu-ray Disc (9 seconds faster than BD50) and 18 seconds for a DVD (2 seconds faster than the BD50).
For Blu-ray Discs with BD-Java based menus, the difference is a bit more noticeable. Pirates of the Caribbean: The Curse of the Black Pearl loads in about 45 seconds on the BD55 versus 56 seconds on the BD50. We measured this by inserting the disc into the tray, pressing play on the BD55 and starting the clock. When the first trailer from the POTC Blu-ray Disc itself appeared on the screen (after the spinning coin), we stopped the clock. As a point of reference, the mighty PS3 from Sony loads that same BD-Java disc in about 40 seconds, so the Panasonic isn't far off. In fact, on "Hitch," the Panasonic was actually about 9 seconds faster than the PS3 and on a standard DVD, the BD55 was 6 seconds faster than the PS3. These load times are easy to live with, particularly with the enhanced picture and sound benefits available on Blu-ray Disc.