Update always there? And no login

I am running the latest version of WordPress and have been seeing this little issue since my last upgrade that didn’t resolve itself with my latest upgrade last night. I am using the auto updater.

1. When I login WordPress never seems to remember my login name. It does however remember the password.

2. There is always an update icon waiting for me in updates upon login, even when everything is up to date.

Does anyone have any advice on how to resolve these? There doesn’t seem to be any issues other than the annoyance to me.

Jay