We just returned from Rome and I wanted to give an update on the ticket situation at the Pantheon:
Tickets are required for entry (€5 euro each). These can be purchased in advance on the official Pantheon website or in person at the ticket office. There does not appear to be a restriction on the number of reservations per time slot. The third option is to buy online when arriving at the site (they have a QR code to the official website you can scan with a smartphone).
We decided not to buy tickets in advance in order to have more flexibility. When we showed up, there were LONG lines for the ticket office by those who also had not reserved in advance.
We had trouble using the official website as multiple credit cards were declined. The trick is to select “Other Payment Methods” and choose one of the PayPal account options. (It will first take you to a third party site regardless of payment option - just enter your email.)
Once we had purchased our online tickets on the spot, with a small ~€1 fee (I believe the credit card option also had a fee), we were able to walk right in!
I hope this is helpful for those who run into the same issue!