You didn't mention what agencies you were listening to that use P25. But I'll start off by giving you a few ideas...
When you are monitoring an obvious P25 digital signal but it is only decoding partially, some of the likely problems could be:
1. Signal strength
It may be that the signal is marginal into your scanner, and so it cannot get a decent decode of the signal all of the time. When it can't get a decent decode, you will hear the P25 data sound interspersed with momentary patches of decoded P25 audio.
2. Interference
If the P25 signal is strong but you are still having difficulty decoding it, it may be that the signal is being interfered with by another strong signal close by in the band.
If what you are experiencing occurs again, immediately after the transmission stops you should make note of whether you hear anything else on the frequency or on a nearby frequency possibly bleeding over. It could be another transmitter on the same frequency interfering (less likely), it could be a signal on an adjacent channel (just up or down in frequency from the frequency you are monitoring), or it could be overload of your receiver by a strong signal somewhere else in the band.
3. Simulcast distortion
Digital signals are sometimes rough if you are attempting to monitor them from several signal sources (multiple transmitters) at the same time.
Simulcast systems are those systems that have transmitters in multiple locations to provide adequate coverage for the agencies that use the system... those transmitters all activate at nearly [but not necessarily exactly] the same time. When you have a transmitter from your north that is 2 miles away, one from your west that is 5 miles away, one from your south that is 8 miles away, all transmitting a digital signal at the same time, the time difference between when the data reaches your scanner from each of those sites, although nearly imperceptible to the naked ear, can be enough of a time difference that the digital data is not received [or not recieved in sequence] at the same exact time, so the scanner has difficulty in putting those packets of data back together in order to decode them and produce your audio.
Do a search on these forums for "simulcast distortion" and you'll find a lot of people discussing it. It is common on P25 trunked systems that are simulcast. Not all digital trunked systems are simulcast - some have completely separate sites that are only activated for radios affiliated with that particular site, rather than all sites transmitting each time a transmission is made into the system.
If you are experiencing simulcast distortion, the best way that most people seem to achieve satisfactory decode is to get a directional antenna that you can point in the direction of the strongest tower (perhaps the one closest to you) or that you can orient in such a way that most of the sites are "nulled" off the sides of the directional antenna.
If you are experiencing interference from on the particular frequency that you are listening to, it could be interference generated internally in the scanner, interference from nearby electronic equipment, etc.
The list above is not a comprehensive list of reasons why you would have difficulty decoding, but they are by far the most popular reasons.
Also, you should make sure you have the latest firmware uploaded to your scanner... Most digital scanners have, over time, numerous versions of firmware provided by the maker. And usually each new version provides some improvement over the previous version. So, check your scanner's firmware and make sure it is the latest. If it isn't, follow the manufacturers instructions for installing the latest.
It will definitely help others to help you if you let everyone know what type of scanner you have, what version of firmware you have, and what P25 signals you are attempting to monitor.
Ok.. this is just a starter for you. I'm sure a lot of people will chime in with useful advice [and perhaps some not so useful advice]. If you have questions, continue to ask them and somebody will respond to them [maybe me, likely somebody else].
Mike