Some stocks are traded a lot and the price graph looks continuous.
Others just jump all the time.
Which metric could I use to filter the stocks that are not continuous? I don't think volume helps much on it.
Well that would be relative to what you are looking to trade.
If you were looking to trade say 1000 share of a company and the average daily volume was 50000, you might consider this stock is liquid enough for you to get in and get out without you moving the price much. But if you were looking to trade say 30000 of the same stock, then you would be trading more than half the average daily volume in one go - this might cause the market to move and cause you to get a bad price buying it and a bad price selling it.
I generally don't want to trade something where my position is more than 5% of the average daily volume.
Another measure of liquidity is the spread between the bid and ask prices. If the spread is 1% or less (for anything around $5 or less) or 0.1% or less (for anything around $100) than the last traded price, then I would consider the liquidity good.
I notice you are looking at minute charts in your examples. Some stocks may look quite liquid on a daily chart and have relatively good volume and small spreads, but as you go down in timeframe, such as you have to a minute chart, the liquidity seems to be quite poor. This is because they might trade within very tight price ranges, so even though you might get good volume traded in one minute the price has not moved in that one minute, so the chart just prints a dash.
Also you are comparing a stock priced in the $160s to a stock trading under $1 on a minute chart. a 10c move on a $160 price stock is nothing, whilst a 0.5c move on a 75c stock is a much bigger move.
So the first thing you need to do is to set parameters on the volume and price of stocks you want to trade (for example I don't trade stocks with an average daily volume below 100000 and with a price below $1). Then you need to decide what time frame you want to trade in. Example, if you want to be a longer term trader you wouldn't be looking at minute charts to choose your stocks.