I can understand why they get predictions about the future wrong, that bit is hard. What gets me is when the prediction for right now is at odds with what is actually happening. It seems like there is a significant delay between sensors on the ground taking a reading and the models being updated.
Most regional models are run at least once an hour and make use of data from sensors up to a few minutes before the model is run. Even if a weather model was perfect, it would still produce incorrect results because models are always started with conditions that do not reflect the true state of the atmosphere. Weather models use other models or earlier runs to produce a best guess at the current state of the atmosphere. The atmosphere model is "adjusted" using the latest sensor, sounding, radar and satellite, data and then the model is run to predict the future. All weather models have to deal with the fact they only have an loose estimate of the state of each 3-D cell in the real atmosphere.
While we have lots of sensors close to the ground, we have very few up high in the atmosphere. The state of the upper atmosphere is rarely measured directly. Balloon soundings are done once or twice a day and only from a few places. The latest soundings have a huge effect on weather model results, so major corrections take about 12 hours if the sounding for an area was not representative of the local state of the atmosphere.
Apart from it being slightly comical when the guy on TV says sun is out but looking through the window I can see rain, it makes short term predictions useless. If they say it will rain this evening when I want to go out but the forecast for right now is wrong, what am I supposed to do with that information?
The best weather models usually get the features right, but are often off in timing. Frontal passages often happen hours from when they are predicted, but they do occur. Use radar and surface sensor data if you want to know current weather. Satellite data are usually less than 30 minutes old. Use model data to get a best guess on the future.
At best you get a vague prediction of the weather in the next few days, but the exact timing of events tends to vary quite a bit from what they say. It doesn't help that in the UK TV weather forecasts are delivered in the most confusing way possible, but fortunately we have the internet now.
Wide spread rain and snow events are the hardest to model or predict as the precipitation falls out in bands which form chaotically. Unless one precisely knows the starting position, one cannot predict the outcome over time. We will never have sensors every N meters in a 3-D grid over the earth so weather predictions will always be off.