Jeans not a problem as far as we recall in the churches, though we probably wouldn't wear them to a Papal Audience or to visit the Scavi under St. Peter's. These sites are revered by hundreds of millions. Regardless of your normal clothing style you'll enjoy your visit more observing these simple signs of respect. In the fall, winter and early spring you'll want to be prepared for rain. For more thoughts on dressing for your European vacation see our notes on Dressing for Success .
Crowds are a bit less and weather is generally more favorable.
The winters are cool to cold, but rarely if ever harshly cold. The Mediterranean climate does bring a bit of rain for much of the year and often provides a dampness to winter temperatures. There's no strong reason to avoid the city at any time, though we've avoided Holy Week because of the throngs over at the Vatican. It's a myth. There's no problem in visiting Rome in August.