As I understand it, the issue from your second point does not make it harder to find the virus, but it removes a marker that allowed to infer the Omicron variant in PCR assays (S-gene dropout). One practical implication is that it makes it harder to decide wether a patient should receive certain monoclonal antibodies that are effective against Delta but not a good use of limited resources against Omicron.
In case anybody is interested:
(Please take with a grain of salt, I'm
not an expert, just interested)
PCR tests are targeting parts of the virus genome, instead of analyzing the whole genome like gene sequencing. Those targets are only detected when an exact match is found. If the target is mutated, it can escape detection.
To ensure infections are not missed in case of mutations, manufacturers usually select multiple targets and at least one target that resides in a stable region that is unlikely to mutate. One example is the N-gene (for the nucleocapsid). The N-gene of SARS-COV-2 is still quite similar to other bat-associated betacoronaviruses like the original SARS-COV-1.
Other genes like the S-gene (for the spike protein) are more likely to mutate. If such a mutation affects a target, S-gene target failure (also called S-gene target dropout) happens. So when a PCR test doesn't find one of its targets but confirms the presence of other targets, this is an indication for a different variant.
This is how the Alpha variant was initially noticed in the UK, before it was confirmed by sequencing. Apparently, the UK just happened to use a test widely that was affected by the S-gene dropout. The UK also sequences a lot more than most other countries.
Like Alpha, Omicron subtype BA.1 has a deletion on the S-gene at 69-70 that causes S-gene dropout on certain PCR tests. This deletion is not present on the wild type, Delta and Omicron subtype BA.2. Therefore Delta and Omicron BA.2 can't be distinguished with those PCR tests, but I guess one could create specialized PCR tests for that purpose. Sequencing also works regardless of variant, but is not as widely available.
Further reading:
About PCR target selection
Manufacturer information of a variant selective test
Reinhard