In the eyes of the general consumer, I'd nominate:
The early rust-out & QC of the '57 cars, which were otherwise pretty amazing at the time. That hurt them for many years.
Generally cheaper interior appearance than the competition.
Sometimes too-cheap materials, like interior vinyls.

Chrysler Corp was justly regarded as an engineering-heavy manufacturer, but I'd bet there was competition among the engineers for cleverness.
Some of the items already mentioned are valid, but try a '60s Ford product for weird ideas & non-interchangeable items: just nuts !

Later on, the crap MP stuff, and their lack of support for their iconic older cars (vs, say, Chevrolet) has marginalized them.

Nevertheless, there's so much great stuff they did, I'd use a few paragraphs to list it all.