Under the Employee Retirement Income Security Act, the vast majority of 401(k) plans are required to purchase a fidelity bond, which protects plan assets from fraud or dishonesty on the part of any person that “handles funds or other property” within the plan, according to the Labor Department.

That required insurance coverage is separate from fiduciary liability insurance, which covers plan fiduciaries against breaches of fiduciary responsibilities that do not amount to fraud. Unlike fidelity bond protections, sponsors are not required by ERISA to carry fiduciary liability insurance.

According to the Labor Department, ERISA “makes it an unlawful act for any person to receive, handle, disburse, or otherwise exercise custody or control of plan funds or property” without being bonded under a fidelity insurance contract.

Specifically, fidelity bonding is usually necessary for the plan administrator, and officers and employees of the sponsor with duties to receive and disburse plan funds.

Fidelity bonding coverage may also be required of service providers and advisors to a plan when their duties involve access to plan assets or decision-making authority that can “give rise to a risk of loss through fraud or dishonesty,” the DOL says.

Related: Top 10 fiduciary errors and how to avoid them

Under ERISA, regulated financial institutions acting as service providers to plans, such as an insurance company or a registered broker-dealer, do not have to be named and covered on a fidelity bond, even if their responsibilities include handling plan funds.

Each person responsible for handling plan funds must be bonded in an amount equal to at least 10 percent of the amount of funds they handled in the preceding year. The Labor Department cannot require a bond to carry more than $500,000 worth of coverage for one plan official. The bonds can be paid for with plan assets.

In an interview, Ryles explained that red-flag data is not limited to plans with more than 100 participants, which are required to file the longer Form 5500, but that the main criteria for the list was that plans have at least $3,000 in assets actively administered.

2. 57,410 plans issued a corrective distribution

According to the most recent available data from the Labor Department, a significant portion of the 401(k) universe was required to issue a corrective distribution under the IRS's nondiscrimination test, which ensures that elective and matching contributions for rank-and-file employees are proportional to contributions from business owners, managers, and other highly compensated employees.

Related: Thousands of 401(k) plans fail non-discrimination tests

By design, as rank-and-file employees save more for retirement, the testing allows highly compensated employees to defer more income to their accounts as rank-and-file employees save more for retirement, according to the IRS.

Two tests — the Actual Deferral Percentage and the Actual Contribution Percentage test — are used to determine the IRS's nondiscrimination provision.

Under both, plans pass the discrimination test if the ADP and ACP for highly compensated employees does not exceed 125 percent for rank-and-file participants.

If plans fail the testing, they are required to make corrective distributions from plan assets back to the affected highly compensated employees within a certain timeframe.

“That can have tax consequences for those employees, and it also means that firms' most highly compensated people are not able to save as much as they want to for retirement,” explained Ryles.

3. 56,275 plans had a high percentage of retirees with assets still in plan

Often, participants leave assets behind in a 401(k) plan when they retire. That means the plan continues to pay administrative costs on those assets, which can increase overall plan expenses, signaling potential inefficiencies in plan design, said Ryles.

Those numbers, and potential inefficiencies, are bound to increase due to several factors. For one, the aging workforce will likely result in more plans harboring retirees' assets.

The Labor Department's fiduciary rule, which is expected to make an impact on the IRA rollover market, is likely to result in more assets staying in-plan post retirement, according to analysis from Cerulli Associates and other industry research.

Related: DOL rule may underestimate 401(k) inflexibility for decumulation strategies

Also, media reports have suggested that some mega-sponsors are encouraging retirees to leave assets in plan, so that the plan has greater leverage negotiating service provider fees.

In the latter case, Ryles said the trend is notable, but limited to outlier cases.

“The overall trend draws from so very many plans that I don't think the metric is being overly influenced by those few, but notable plans, that are encouraging participants to keep assets in plan,” he said in an interview.

The bottom line to be drawn from the data is that many sponsors may be paying to administer retiree assets when it is not in the plan's best interest to do so, Ryles noted.

4. 32,354 plans experienced reduced employer contributions

When employers reduce, or eliminate matching contributions, it is often an indication that the sponsor is in financial trouble.

Related: Why doesn't your company want you to put more into your 401(k)?

Analysis commissioned by the Labor Department in 2013 shows that participants saw median matching contributions fall 13 percent from 2008 and 2009, as the economy went into recession after the financial crisis.

A reduction in match, if necessary, may require advisors to step up education efforts to ensure participants are deferring the most they can to their retirement accounts.

5. 28,251 plans showed a history of having to make corrective distributions

This flag suggests that plans that consistently fail the IRS's nondiscrimination testing could be suffering from poor plan administration.

“Additional participant education may be called for to increase the contribution rate of non-highly compensated employees,” Ryles said.