Shouldn't you divide this by employment to try and normalize this. A 350,000
level of claims is now a smaller share of employment then it was a decade ago
so it is not a severe negative or positive.

It is quite an unreliable metric in terms of revisions alone, no? The well publicized losses in the auto industry and manufacturing suggest that this stat should be rising. But the official releases purport to measure offsetting gains in other sectors, professional services in particular. Incredibly, within that sector, rising real estate growth. Which could be true as those terminated auto workers decide that a 6 week RE licence might be worth the trouble.
But the offsetting job gain here masks the reality that the lost manufacturing job is equal to the new real estate job. Not really.
Neglecting to account for this character fosters the view that the economy is still growing and healthier than it is.
Similarly the Owners Equivalent Rent masks the size and importance of housing market on the CPI which keeps government entitlement payments lower, but overstates your capacity to spend when that housing market which has supported all that consumption, is declining. [Are we starting to see this in the credit card numbers?]

Why should we give the unemployment stats much weight?
Partly because it is this number in our face, a marketing artifact with a history of being in our face.
Partly because we just love to squeeze anything and revel in "tightening" or "loosening" whatever fleshy thing you put out there. [Check out interest rates and see if it ain't so.] We B not Masters of the Universe yet, but clearly, we own the title, Master Squeezers.

charts is right. If unemployment stats bulged to 5%, we would know that real staggering unemployment levels had even spread to the BLS for this erroneous bulge to have escaped their notice.