One huge problem with the house is that you really are just about as removed from your house rep as you are the executive branch (and certainly the aristocratic Senate, with its archaic 6 year terms). The country has expanded a great deal, and yet the house is capped at 435 (an arbitrarily established number I should add).
An excellent solution to me is to acknowledge the telecommunications revolution, and allow remote voting on national legislation, this will also allow the expansion of the house to a much larger number.
The clear and obvious advantages to a house of 4350 rather than 435 is that gerrymandering would be greatly reduced (though not impossible over time, I will concede) and local control over reps would be increased because there would be much smaller district sizes (right now the average district is well over 600k per rep. The second advantage here is that the problem of the 20th century was that political candidates were privately financed by the interests that privately control the country. So to pay off 435 is manageable, to a pay off 4350 is much costlier, and to pay off 43,500 even more so. Voting today is done on financial and party line basis...there is not enough of an advantage to be found in the networking and compromise side to outweigh the expansion of the house of representatives into something that can actually represent the varied people's interests in the country.