This report to congress says:

Finally, nine of the 50 risks currently tracked by the project are related to the more than 300 single points of failure aboard the observatory

Being a report for non technical people, I can't find any details on in the report and I'm struggling to find details elsewhere.

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    $\begingroup$ Your title says single points of failure but the body says points of failure, what are you actually asking? $\endgroup$ – GdD May 14 at 10:43
  • $\begingroup$ Well spotted @GdD, I meant single points of failure and have edited accordingly $\endgroup$ – Krish May 14 at 10:47
  • $\begingroup$ 300 single points of failure seems like a lot to me @Krish, considering the amount of redundancy they build in. Are there any actual sources claimed by these people, or would you consider them in the know? $\endgroup$ – GdD May 14 at 10:56
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    $\begingroup$ If you have a source please pull the relevant text out and post it in your question, also put in the link. You'll get better answers with more information in your question. $\endgroup$ – GdD May 14 at 11:02
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    $\begingroup$ @CarlWitthoft - Other parts of NASA use the term FMECA (failure modes, effects, and criticality analysis), or just FMEA (failure modes and effects analysis), or fault tree (which is essentially an upside-down FMEA tree). $\endgroup$ – David Hammen May 14 at 23:40

Synthesising information from these (1 2) reports to congress:

From the 2015 source:

According to project officials, there are over 100 different ways that a failure could occur, referred to as single point failure modes, across hundreds of individual items in the observatory. Each of these could result in a loss of minimum mission objectives, and thus needs to be fully tested and understood. Nearly half of the single point failure modes involve the deployment of the sunshield.

From the 2020 source:

The project found that certain bolts, determined to be deficient on another Northrop Grumman program, were used during the construction of the observatory. A study of this issue found that the bolts used did not meet specifications and could pose a mechanical strength risk. The unused bolts have been identified and isolated, but 501 were installed in the observatory. NASA is performing strength testing to determine if the bolts are strong enough, but some of the deficient bolts may need to be replaced, pending the findings of these tests.

The project reported in August 2019 that grounding straps on the spacecraft’s momentum flap came loose during vibration testing. This flap will act as balance against solar pressure that could cause unwanted movement of the observatory while in orbit. Observatory level vibration testing cannot begin until the flap is removed, repaired, and replaced aboard the spacecraft.

In September 2019, the project found that a non-explosive actuator on one of its membrane retention devices did not fire as planned. These devices, which help to unfurl the sunshield of the spacecraft, are supposed to be electrically redundant, but only one of the two mechanisms used to fire the actuator worked during the test. The program reports that there are approximately 180 actuators on the JWST and the failure of any one of these actuators could result in the total loss of JWST science mission objectives. If the redundancy for the actuators is reduced, it would have a major impact on system reliability.

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    $\begingroup$ That last one's pretty scary. $\endgroup$ – Organic Marble May 18 at 12:42

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