Yes, Rockstar has admitted that Grand Theft Auto Online has not been running smoothly. And it plans on releasing a title update tomorrow that should "address commonly reported issues" with the newly-released multiplayer mode. "We hope to have it out for download as soon as tomorrow," the company said on Twitter.
This page is keeping track of the most common problems affecting GTAO players. Many are network issues caused by heavy demand by players. However, there's also the tutorial race bug, which makes it impossible to get past the initial GTAO race. There are some workarounds, however:
Some players have reported being able to get into the Tutorial race by re-downloading the Title Update, which can be deleted from Xbox Home or the PS3 XMB (Game Data Utility, NOT save data). Others reported having luck by selecting "Swap Character" from the Online tab within the pause menu, deleting the character that was unable to get into the tutorial, and then creating a new character. Going into GTAO in Solo mode may also help to allow completion of the tutorial. Some who were experience this issue have been able to get in just by trying again later.