The federal health-care exchange that opened a dozen days ago is marred by snags beyond the widely publicized computer gridlock that has thwarted Americans trying to buy a health plan. Even when consumers have been able to sign up, insurers sometimes can’t tell who their new customers are because of a separate set of computer defects.

The problems stem from a feature of the online marketplace’s computer system that is designed to send each insurer a daily report listing people who have just enrolled. According to several insurance industry officials, the reports are sometimes confusing and duplicative. In some cases, they show — correctly or not — that the same person enrolled and canceled several times on a single day.

The ability of consumers to sign up for a health plan, and the ability of the insurers to know who they are covering, is key to the success of the federal law that will for the first time require most Americans to have health insurance starting Jan. 1. The Web site is the main path for millions of Americans in 36 states to purchase new coverage.

The flawed enrollment reports illustrate that the site is bedeviled by problems that go beyond what the Obama administration has acknowledged in explaining the creaky performance of the exchange so far.

At the White House and the Department of Health and Human Services, officials have portrayed the exchange as a victim of its own popularity, with a larger-than-expected crush of Americans rushing to a Web site that wasn’t built to accommodate so many people at once.

That explanation puts the focus up front — on the servers and software that help consumers take the first step of registering for an account. Evidence is emerging from the insurance industry and elsewhere, however, that the exchange also has flaws that show up further along in the process — as consumers try to check whether they qualify for federal subsidies and as insurers try to find out who has enrolled.

For instance, one major insurance carrier, Cigna, sent a notice Wednesday to insurance brokers instructing them to wait until November to try to sign up customers who might qualify for a subsidy, according to Joseph Mondy, a Cigna spokesman. He said that the company does not yet trust the reliability of the part of the exchange that is supposed to calculate the tax credits that will, for the first time, help some Americans pay for private health coverage.

Cigna is one of the insurers that has built its own online “portal” for brokers to use, but that portal must communicate with the federal exchange to find out about a potential subsidy.

Cigna is selling health plans via the federal exchange in four states: Arizona, Florida, Tennessee and Texas. Mondy said the carrier has seen “multiple enrollments” coming through for the same customer on the same day.

A Blue Cross Blue Shield plan in a Southern state said that it has also gotten simultaneous reports of the same consumers enrolling as of Jan. 1 and cancelling as of Dec. 31, 2014.

“It’s a glitch that . . . needs to be fixed,” said a spokesman for the plan, who, like most insurers interviewed, spoke on the condition of anonymity to avoid antagonizing the Obama administration.

Compounding the confusion, these electronic enrollment files are missing a critical element that they were built to include: a time stamp that would let a health plan track whether a consumer’s last step on the site was to actually sign up.

Insurers are uncertain of the cause of the flaws, with some speculating that the exchange cannot consolidate consumers’ moves through the Web site as they shop for and ultimately choose a health plan. Others say the problem could be unrelated software errors.

Federal health officials declined to discuss the problem with the enrollment reports. “As individual problems are raised by insurers, we work aggressively to address them,” said Brian Cook, a spokesman for the Centers for Medicare and Medicaid Services, the branch of HHS that is overseeing the insurance exchange.

Meanwhile, the government has tweaked the exchange to deal with the initial problem — accessing the heavily used site — to try to make it easier for shoppers to obtain information without going through the sometimes cumbersome process of registering for an account.

Starting Thursday, a new tool points consumers more directly to a list of the health plans in their community and sample prices. Before, this information was on the site only in an Excel spreadsheet that was hard to find and to understand.

Obama administration officials insisted that this was not a major change to the Web site, because consumers still need to create an account to find out about subsidies and the specific costs of various health plans for people their age.

The initial bottleneck that prevented people from getting onto the site has cleared to some degree. And the seriousness of insurers’ trouble with the enrollment reports will depend on how long the problem persists.

The exchange’s enrollment period lasts for six months starting Oct. 1. Plans start to take effect Jan. 1.

One insurance industry official familiar with the daily reports, known as “834s,” said that they rely on relatively old technology.

Rather than transmitting a file whenever a consumer enrolls, the reports are sent to each insurance carrier in a daily batch at 6 p.m.

Also, the reports contain a “stack” for each consumer, so that if a person picks a health plan, then retypes his or her phone number, two reports are generated.

Beginning in December, health officials intend to run a monthly comparison of the federal list of enrollees against the insurers’ lists. However, one insurance industry official said that the computer system needed to perform that comparison has not been tested.

The flawed enrollment reports result from one of several design and programming issues that have been emerging in recent days, according to technology consultants, health-care advocates and academics who have been monitoring the rollout of the exchange.

For some consumers, the confusion begins with the screen that lets them create a user name.

It asks users to “Choose a user name that is 6-74 characters long and must contain a lowercase or capital letter, a number, or one of these symbols _.@/-”. It has been unclear to some whether they need a letter plus a number or symbol, or whether letters or numbers or symbols are sufficient.

Some consumers are discovering they cannot erase profiles they created by mistake, while others are encountering error messages telling them that profiles they created do not exist. Still others find that when they click on a button to move to another screen, they cannot tell whether the system is stuck or simply slow, because the site does not show them an hourglass or any other sign that a step is underway.

James Turner, a software engineer from Derry, N.H., said he has spent seven hours since Oct. 2 trying to enroll but keeps encountering issues that make have made it impossible for him to complete the application. Turner, 51, one of a number of software engineers who have written online critiques of the system, said the most infuriating one involves his wife. According to the system, he said, “I have four spouses.”

He said it has been impossible to delete the phantom family members from his profile.

Some Americans, however, are managing to enroll. Norbert Crabtree, 46, an accounting consultant in South Carolina, logged on to at 4:30 a.m. Tuesday and finished enrolling about 90 minutes later. The main hitch, he said, was that “they were asking me security questions about a street I lived on 20 years ago. I got that wrong and got kicked out once.”

After a second pass through the security questions, Crabtree said he “swept through” the rest of the application. He enrolled in a plan from Blue Cross Blue Shield with a $450 monthly premium.

He tried calling the insurer shortly afterward, but a representative told him they didn’t yet have enrollment data.

The next morning, someone from the insurer called to say that he was, in fact, enrolled.

Sarah Kliff and Sandhya Somashekhar contributed to this report.