Mkeith has answered the question as asked, i.e. what are the main disadvantages of HVDC distribution. A "counter-answer" to that by helloworld922 (the next most-voted answer here currently) points in the direction of a bunch of cases where HVDC is/was used. All these engineers couldn't have been crazy, so I think it's important to actually explain here when HVDC makes sense. (That would have been a better question than what the OP asked, by the way.)
To start, there are some cases where AC would be almost infeasible. This includes connecting power AC grids that operate asynchronously with respect to each other, such as connecting 50 and 60 Hz systems; it happens in Japan for example: Eastern Japan uses 50Hz and Western Japan uses 60Hz. There are actually a few more niche applications where HVDC is the only reasonable choice, but they're not easy to explain to neophytes in a few words. If you want a more detailed list (with real-world examples), Delea and Casazza's Understanding Electrical Power System has a longer list.
Leaving aside such niche cases, I think it's important to emphasize that there is a total cost optimization that can (and in fact should) be performed when deciding whether AC or DC should be the transmission method for a power line. The two main factors are the cost of the line itself (cables, towers if applicable, e.g. not undersea) and the cost of the terminals. Generally, the DC transmission cables cost less than those of equivalent power for tri-phase AC. This happens for a reason that is easy to explain: you need fewer wires for DC than three-phase AC, but the insulation for the AC wires (and this may be just the air gap, but that translates into tower costs) needs to withstand the peak AC value, while you're only benefitting from transmitting "RMS power" (more correctly, average power corresponding to the RMS voltage) at AC. On the other hand, the terminating power electronics cost more for HVDC than the AC transformers, but why this happens isn't easy to summarize, none the least because the two terminating technologies are different.
This total cost optimization actually gives you the main application of HVDC today: transmitting large amounts of power over long distances (and by that meaning with no tapping/interruption). The typical values where HVDC is more economical than AC is transmitting more than 500MW over more than 500km (according to Delea and Casazza). Many (if not most) of the examples from the Wikipedia list (linked in helloworld922's answer) are of this kind. It shouldn't be a surprise than such examples are from China, Canada or Australia. In Europe, most of the medium/large HVDC transmission lines are undersea cables.
Below is what a synthetic (meaning textbook-level rather than real-world) optimization example looks like for a pre-determined power level, thus in which only the cost vs. transmission distance is plotted; it is excerpted from Kim et al. HVDC Transmission, the first chapter of which is freely available.
For a concrete cost perspective, here are some values (according to Larruskain et al..) for what is close to the lowest power for which HVDC terminal components are made:
- Thyristor converter, 50 MW, 100kV. Approximate per unit value is: 500 EUR/kW
- IGBT converter pair, 50 MW, +/-84kV. Approximate per unit value is: 150 EUR/kW
- Transformer, 50 MVA, 69kV/138kV. Approximate per unit value is: 7.5 EUR/kVA
Given the 20x-60x price ratio between a rectifier and a transformer at 50 MW, it is obvious why HVDC doesn't scale down to lower powers.