Wireless communication under water
Any of the underwater acoustics companies would be able to advise on likely performance and potential problems with a bit of detail about your application, typical considerations (as others have noted) include:


There is a trade off between range and data rates (low frequencies allow longer range but lower data rates)
Power supplies can be a limitation, energy per bit for acoustic communications underwater is substantially higher than RF communications in air, and usually there is no power supply network nearby
Environmental issues need to be taken into account (frequencies used by marine life for communications and 'sonar' are well known, equipment can be selected to avoid interference)
Size and weight of equipment (again, usually led by battery pack limitations)
Efficiency (e.g. a directional transducer will increase power efficiency and/or remove some noise off axis, but require some alignment between transmitter and receiver)
Physical effects (refraction, reflections, propagation delay) typically limit maximum performance (e.g. thermal gradients in deep water typically refract signals upwards, limiting maximum range)


If you add more details about your application, you might get more specific advice about the real-world problems you might face, for example can you give a little bit more information on:


Water depth
Position of the modems (surface or sea-bed)
Location (open seas have different acoustic effects to harbours, narrow channels, or areas where fresh water flows into the sea)
Noise sources in the area (are the modems attached to vessels with engines, or remote from man-made noise)
Data transfer rates that you are aiming for


There are a number of suppliers of equipment, targeted at a range of applications, from modem suppliers through to acoustic positioning and control (off the top of my head, these include Kongsberg, Nautronix, Sonardyne, Linkquest, Evologics (in no particular order!)).  Each optimises performance for their application area so there isn't a list of 'major problems' that you can consider, each trades off one limitation for another.

[Disclosure, I work for one of the above companies, but I'm confident there's nothing in this answer which any of the others would disagree with]