Either that, or the markers are fine but the lines are slightly offset from the intended points.

Possibly related to #7233?

oops, yeah I just found that and #8533

mark as duplicate?

No problem. Thank you for opening the ticket ;). I did not follow the latest evolution of those news, so I do not know if there were some improvements on that topic :/ (and pinging @anntzer who tried to tackle those questions IIRC ^^).

Marking as duplicate and closing as the issue seems similar to the ones reported in #7233, #7262, #7624, and #8533. Anyone please remove the flag and reopen the thread (or ask for it) if you disagree.

I just want to note, while there certainly is the annoying issue of marker stamping present here, most of the mismatch from the example comes from the wrong linspace in use. If you want points spaced by 0.05, you need to use 41 points between -1 and 1, not 40.
So with t = np.linspace(-1,1,41) we get

which is indeed not optimal, but not as bad as it seems at first sight.

thanks but that doesn't concern me, it's only the fact that the markers are off-center compared to the lines joining them.

There is no one working on fixing this for the default Agg-based backends (AFAIK), although the issue is well understood. You may want to try the cairo based backends, which don't have this specific issue (not sure you can activate them with jupyter notebook? Perhaps @jklymak knows something here as I know he uses the notebook); alternatively, I wrote https://github.com/anntzer/mplcairo (another cairo based backend) in particular to fix the issue.

You may use the Cairo backends in jupyter just as other backends, matplotlib.use("TkCairo"). The output will of course be a figure window invoked by plt.show(). There is no "inline"-cairo backend, but one may of course quickly tinker one together:

import matplotlib
matplotlib.use("TkCairo")

import numpy as np
import matplotlib.pyplot as plt

t = np.linspace(-1,1,41)
fig = plt.figure()
plt.plot(t,t**3 - 0.75*t,'.-',linewidth=0.3, markersize=3)
plt.grid(True)

def inline_show(fig=None):
    import io
    from IPython.display import Image, display
    fig = fig or plt.gcf()
    buff = io.BytesIO()
    fig.savefig(buff)
    buff.seek(0)
    display(Image(data=buff.getvalue()))
    plt.close(fig)
    
    
inline_show(fig)  

The same approach can also be used with the usual AGG backends. Because the stamping issue is more pronounced the smaller the dpi, one may save a high-dpi version of the figure and display it with lower width in the notebook.

%matplotlib inline  # "inline is Agg based
import numpy as np
import matplotlib.pyplot as plt

t = np.linspace(-1,1,41)
fig = plt.figure()
plt.plot(t,t**3 - 0.75*t,'.-',linewidth=0.3, markersize=3)
plt.grid(True)

def inline_show(fig=None):
    import io
    from IPython.display import Image, display
    fig = fig or plt.gcf()
    buff = io.BytesIO()
    fig.savefig(buff, dpi=400)
    buff.seek(0)
    display(Image(data=buff.getvalue(), width=480))
    plt.close(fig)
    
inline_show(fig)

Was this fixed? I'm not sure if I'm still seeing it or something else:

The dots seem to be below the line more often than not:

Unfortunately we have not increased the number of marker stamps yet. The linked issues are still open.

The issue can be ameliorated by increasing the DPI.