...and this morning it works.

I've plugged in a new Onion, and can't run an opkg update.

I've tried the old solution recommended here, and it cleans out a line or two of errors from the opkg update, but leaves plenty of errors still:
Re: "Signature check failed." /var/opkg-lists/chaos_calmer_packages.

Here's the new output of attempting opkg update since removing the signature check:

Downloading http://downloads.openwrt.org/chaos_calmer/15.05.1/ar71xx/generic/packages/base/Packages.gz.
wget: '/usr/lib/libpcre.so.1' is not an ELF file
wget: can't load library 'libpcre.so.1'
Downloading http://repo.onion.io/omega/packages/Packages.gz.
wget: '/usr/lib/libpcre.so.1' is not an ELF file
wget: can't load library 'libpcre.so.1'
Downloading http://downloads.openwrt.org/chaos_calmer/15.05.1/ar71xx/generic/packages/packages/Packages.gz.
wget: '/usr/lib/libpcre.so.1' is not an ELF file
wget: can't load library 'libpcre.so.1'
Collected errors:
 * opkg_download: Failed to download http://downloads.openwrt.org/chaos_calmer/15.05.1/ar71xx/generic/packages/base/Packages.gz, wget returned 16.
 * opkg_download: Failed to download http://repo.onion.io/omega/packages/Packages.gz, wget returned 16.
 * opkg_download: Failed to download http://downloads.openwrt.org/chaos_calmer/15.05.1/ar71xx/generic/packages/packages/Packages.gz, wget returned 16.