Google said a "majority" of users were affected by the short-term software problem.
While people could still access and use Gmail many people saw "unexpected behaviour" because of the problem.
Many reported the errors via Twitter seeking clarification from Google about what had gone wrong.
The error messages started appearing early on 4 April and hit people trying to send email messages from Gmail and some of the firm's messaging apps.
The problems arose because Google had neglected to renew a security certificate for Gmail and its app services. The certificate helps the software establish a secure connection to a destination, so messages can be sent with little fear they will be spied upon.
Google's own in-house security service, called Authority G2, administers the security certificates and other secure software systems for the search giant.
Information about the problem was posted to status pages Google maintains for its apps and email services.
In the status message, Google said the problem was "affecting a majority of users" who were seeing error messages. It added that the glitch could cause programs to act in "unexpected" ways.
The problem was resolved about two hours after it was first noticed.
The glitch comes soon after Google started refusing security certificates issued by the China Internet Network Information Center (CNNIC). Google said a security lapse by the CNNIC meant the certificates could no longer be trusted. CNNIC called the decision "unacceptable and unintelligible".
Gmail users around the world saw errors and safety warnings over the weekend after Google forgot to update a key part of the messaging software.