Try-catch: is this acceptable practice?

Terrible, indeed. Swallowing an exception like this can be dangerous. How will you know if something bad has happened?

I'd feel better if the vendor wrote comments to document and acknowledge it ("We know what we're doing"). I'd feel even better if there was a strategy apparent in the code to deal with the consequences. Wrap it in a RuntimeException and rethrow; set the return value to an appropriate value. Anything!

"All over the place"? Are there multiple try/catch blocks littering the code? Personally, I don't like that idiom. I prefer one per method.

Maybe you should find a new vendor or write your own.

This is indeed terrible practice. Especially the catching of Exception rather than something specific gives off a horrible smell - even a NullPointerException will be swallowed. Even if it is assured that a particular thrown exception is of no real consequence, one should always log it at the very least:

try {
    // code
}
catch (MyInconsequentialException mie) {
   // tune level for this logger in logging config file if this is too spammy
   MY_LOGGER.warning("Caught an inconsequential exception.", mie);
}

However it is unlikely an exception is completely meaningless in this situation. I recommend researching exactly what exception(s) the application's code is intending to swallow here, and what they would really mean for the execution.

One important distinction is whether the try/catches are used to swallow checked exceptions. If this is the case, it probably indicates extreme apathy on the programmer's part - somebody just wanted his/her code to compile. At the least, the code should be amended:

try {
   // code
}
catch (SpecificCheckedException sce) {
   // make sure there is exception logging done farther up
   throw new RuntimeException(sce);
}

This will rethrow the exception wrapped in an unchecked RuntimeException, effectively allowing the code to compile. Even this can be considered a bandaid however - best practice for checked exceptions is to handle them on an individual basis, either in the current method or farther up by adding throws SpecificCheckedException to the method signature.

As @Tom Hawtin mentioned, new Error(sce) can be used instead of new RuntimeException(sce) in order to circumvent any additional Exception catches farther up, which makes sense for something that isn't expected to be thrown.

If the try/catch is not being used to swallow checked exceptions, it is equally dangerous and should simply be removed.